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Similar Question 1
<p>For each line segment,</p> <ul> <li>count grid units to find the rise</li> <li>count grid units to find the run</li> <li>determine the slope</li> </ul> <img src="/qimages/1161" />
Similar Question 2
<p>A regular hexagon has six sides of equal length. One is drawn on a grid as shown. Determine the slope of the line segment from the centre to the vertex indicated. Explain your reasoning.</p><img src="/qimages/6877" />
Similar Question 3
<p>Identify the x- and y-intercepts of each graph, if they exist.</p><img src="/qimages/22028" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>A regular hexagon has six sides of equal length. One is drawn on a grid as shown. Determine the slope of the line segment from the centre to the vertex indicated. Explain your reasoning.</p><img src="/qimages/6877" />
<p>Write the equation of the line through each point. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle (-2,1) ; </code> perpendicular to <code class='latex inline'>\displaystyle 3 x+y=1 </code></p>
<p>Write the equation of each line in question 4.</p>
<p>Determine whether or not the following sets of points form right triangles. Justify your answers with mathematical reasoning. </p><p><code class='latex inline'>M(-4,2), N(-1,4), O(1,1)</code></p>
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>e) <code class='latex inline'> 3x = 9</code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22035" />
<p>Calculate the slope of each line segment, where possible.</p><img src="/qimages/144167" /><p><code class='latex inline'>GH</code></p>
<p>Do the points in each set lie on the same line? Explain your answer.</p><p><code class='latex inline'>\displaystyle G(3,5), H(-1,3), I(7,7) </code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (-4,-3) </code> and <code class='latex inline'>\displaystyle (7,1) </code></p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>x-y+2=0</code></p>
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle 8 x+6 y=5 </code></p>
<p>Determine the slope of each object.</p><img src="/qimages/1159" />
<p>Find an equation for the line containing line segment AB where <code class='latex inline'>A(1,0)</code> and slope of AB is perpendicular to the line <code class='latex inline'>y = -2x -2</code></p>
<p>Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.</p><p><code class='latex inline'>\displaystyle (-2,6),(0,2),(1,0) </code></p>
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'>m=-\dfrac{1}{2}, m=\dfrac{1}{2}</code></p>
<p>Graph each equation.</p><p><code class='latex inline'>\displaystyle y=\frac{2}{3} x+4 </code></p>
<p>Determine whether or not the following sets of points form right triangles. Justify your answers with mathematical reasoning. </p><p><code class='latex inline'>D(-2,5), E(2,3), F(3,-2)</code></p>
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (a,-b),(-a,-b) </code></p>
<p>For the line: </p> <ul> <li>identify the slope and the y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>2x+3y+6=0</code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (-5,-7) </code> and <code class='latex inline'>\displaystyle (0,10) </code></p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle \frac{A}{D} x+\frac{B}{D} y=\frac{C}{D} </code></p>
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle -3 x+2 y=7 </code></p>
<p>Malena says that (5, 1) is a solution of <code class='latex inline'>y=2x+3</code>. Bryan says it is not a solution.</p><p><code class='latex inline'>\displaystyle \begin{array}{cc}\text { Malena } & \text { Bryan } \\ y=2 x+3 & y=2 x+3 \\ 5=2(1)+3 & 1=2(5)+3 \\ 5=5 & 1 \neq 13\end{array} </code></p><p>Who is correct?</p>
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>y=3x+5</code></p>
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>b) <code class='latex inline'> 2x+y=8</code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22033" />
<p>The slope and the y-intercept are given. Write the equation and graph each line.</p><p>slope= <code class='latex inline'>\frac{2}{5}</code>, y-intercept= -1</p>
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'>m=0.4, m=\dfrac{2}{5}</code></p>
<p>Write an equation for each line. Each interval is 1 unit.</p><img src="/qimages/88551" />
<p>Write an equation in standard form of the line with an x-intercept of 3 and a y-intercept of 5.</p>
<p>Find the slope and the y-intercept of each line.</p><p> <img src="/qimages/22073" /></p>
<p>Find an equation for a line perpendicular to <code class='latex inline'>y = 2x - 3</code>, passing through the origin.</p>
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24683" />
<p>Determine whether or not the following sets of points form right triangles. Justify your answers with mathematical reasoning. </p><p> A(1,3), B(5,1), C(6,3)</p>
<p>Find the intercepts and graph each line.</p><p><code class='latex inline'>\displaystyle 5 x+7 y=14 </code></p>
<p> Determine the x- and y-intercepts of each line. Then, graph the line.</p><p><code class='latex inline'>\displaystyle 3x - 4y =12 </code></p>
<p>For each graph, plot the intercepts and graph the line.</p><img src="/qimages/22031" />
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (-4,10) </code> and <code class='latex inline'>\displaystyle (-6,15) </code></p>
<p>Write the equation of a line with the given slope and y-intercept. Then, graph the line.</p><p><code class='latex inline'>m = -2, b = 3</code></p>
<p>Triangle LMN has vertices L(-1,2) and M(-4,-1). </p><p>a) Find the coordinates of N such that triangle LMN is a right triangle. </p><p>b) Is there more that one solution? Explain. </p>
<img src="/qimages/44410" />
<p>Write an equation for each line. Then graph the line.</p><p><code class='latex inline'>\displaystyle m=-\frac{3}{2} </code>, through <code class='latex inline'>\displaystyle (0,-1) </code></p>
<p>Write an equation of the line in slope-intercept form.</p><img src="/qimages/44384" />
<p>Ontario. In one part of it, there is a very steep slope. Two of the letters in the name of this city can be found by determining the slope and the y-intercept of the graph shown.</p><img src="/qimages/1204" />
<p>WRITING A line passes through the points <code class='latex inline'>\displaystyle (0,-2) </code> and <code class='latex inline'>\displaystyle (0,5) </code>. Is it possible to write an equation of the line in slope-intercept form? Justify your answer.</p>
<p>State the equation and sketch the graph of the line described below.</p><p>passing through <code class='latex inline'>(-3, -4)</code> and <code class='latex inline'>(\frac{5}{3}, -\frac{5}{3})</code></p>
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle 9 x-2 y=10 </code></p>
<p>Error Analysis A classmate</p><p>found the slope between</p><p>two points. What error did</p><p>she make?</p><img src="/qimages/88416" />
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (1,6) </code> and <code class='latex inline'>\displaystyle (2,8) </code></p>
<p>A triangle has vertices <code class='latex inline'>C(1, 4), D(-2, 2)</code>, and <code class='latex inline'>E(3, 1)</code>.</p><p><strong>(a)</strong> Draw <code class='latex inline'>\triangle CDE</code>.</p><p><strong>(b)</strong> Use analytic geometry to verify that <code class='latex inline'>\angle C</code> is a right angle. </p>
<p> Calculate the slope of the line through each pair of points. </p><p><code class='latex inline'>(2, 7), (-3, -8)</code></p>
<p>Explain why the slope of a vertical line is called &quot;undefined.&quot;</p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (-6,-1) </code> and <code class='latex inline'>\displaystyle (-4,-6) </code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>3x+2y-6=0</code></p><p><code class='latex inline'>2x-3y+6=0</code></p>
<p>Write the equation of a line with the given slope and y-intercept. Then, graph the line.</p><p><code class='latex inline'>m = 0, b = 2</code></p>
<p>A cross-country ski area classifies its courses based on the range of slopes. If the slopes are less than 0.09, the course is classified as easy. For slopes between 0.09 and 0.18, the course is intermediate. For slopes greater than 0.18, the course is difficult. For a ski hill 10 m tall, what range of horizontal runs is appropriate for each classification?</p>
<p>Identify the slope and y-intercept of each line, if they exist.</p><p>a) <code class='latex inline'>y=2</code></p><p>b) <code class='latex inline'>x=3</code></p><p>c) <code class='latex inline'>y=-4</code></p><p>d) <code class='latex inline'>x=-1</code></p>
<p>Graph each equation using x- and y-intercepts.</p><p><code class='latex inline'>\displaystyle x+y=4 </code></p>
<p>Vocabulary Tell whether each equation is in slope-intercept, point-slope, or standard form.</p><p>a. <code class='latex inline'>\displaystyle y+2=-2(x-1) \quad </code> b. <code class='latex inline'>\displaystyle y=-\frac{1}{4} x+9 </code></p><p>c. <code class='latex inline'>\displaystyle -x-2 y=1 \quad </code> d. <code class='latex inline'>\displaystyle y-3=4 x </code></p>
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=\dfrac{1}{2}x +1</code></p><p><code class='latex inline'>y=\dfrac{1}{2}x-1</code></p>
<p>Find the slope of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle \left(-\frac{1}{2},-\frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle (-3,-4) </code></p>
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=3x-2</code> </p><p><code class='latex inline'>y=2x-3</code></p>
<p>Find the intercepts and graph each line.</p><p><code class='latex inline'>\displaystyle x-4 y=-4 </code></p>
<p>Which point lies on the line given by <code class='latex inline'>y=3x-5</code>?</p><p>A. (1, -2)</p><p>B. (0, 5)</p><p>C. (1, 2)</p><p>D. (4, 3)</p>
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (2 a, b),(c, 2 d) </code></p>
<p>Graph each equation.</p><p><code class='latex inline'>\displaystyle x+3=0 </code></p>
<p>Given a point <code class='latex inline'>A(2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope = <code class='latex inline'>-\displaystyle{\frac{2}{3}}</code></p>
<p>Plot the points <code class='latex inline'>\displaystyle \mathrm{E}(4,5), \mathrm{F}(7,0) </code>, and <code class='latex inline'>\displaystyle \mathrm{G}(1,-4) </code>. Find all locations of the point <code class='latex inline'>\displaystyle \mathrm{H} </code> so that <code class='latex inline'>\displaystyle \mathrm{EFGH} </code> is a parallelogram.</p>
<p>Write an equation of each line.</p><p>slope <code class='latex inline'>\displaystyle =-1 ; </code> through <code class='latex inline'>\displaystyle (-3,5) </code></p>
<p>Calculate the slope of each line segment, where possible.</p><img src="/qimages/144167" /><p><code class='latex inline'>AB</code></p>
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (3,2),(8,12) </code></p>
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=4x+2</code></p><p><code class='latex inline'>y=-\dfrac{1}{4}x+1</code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=x+2</code></p><p><code class='latex inline'>y=-x</code></p>
<p>Calculate the slope of each line segment.</p><img src="/qimages/132107" /><p>a) <code class='latex inline'>\displaystyle \mathrm{AB} </code></p><p>b) <code class='latex inline'>\displaystyle \mathrm{CD} </code></p><p>c) <code class='latex inline'>\displaystyle \mathrm{EF} </code></p><p>d) <code class='latex inline'>\displaystyle \mathrm{GH} </code></p>
<p>Write an equation of each line in standard form.</p><p>the line perpendicular to <code class='latex inline'>\displaystyle -2 x+3 y=9 </code> through <code class='latex inline'>\displaystyle (-1,-3) </code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (1,2) </code> and <code class='latex inline'>\displaystyle (2,3) </code></p>
<p>The line has the same slope as <code class='latex inline'>\displaystyle 4 x-y=5 </code> and the same <code class='latex inline'>\displaystyle y </code> -intercept as the graph of <code class='latex inline'>\displaystyle 3 y-13 x=6 </code>.</p>
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle 5 x+y=4 </code></p>
<p>Explain how the slopes of parallel lines are related. Create an example to support your explanation.</p>
<p>The area of the shaded region is 12 square units. What is the slope of the line through AB?</p><img src="/qimages/1170" />
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=x+1</code></p><p><code class='latex inline'>y=-x+1</code></p>
<p>Write an equation of each line in standard form.</p><p>the line parallel to <code class='latex inline'>\displaystyle y=-3 x+4 </code> through <code class='latex inline'>\displaystyle (0,-1) </code></p>
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (0,-1) </code> and <code class='latex inline'>\displaystyle (3,-5) </code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (1,6) </code> and <code class='latex inline'>\displaystyle (8,-1) </code></p>
<p>Classify each pair of lines as parallel, perpendicular, or neither. Explain.</p><p><code class='latex inline'>y = \frac{3}{4}x + 2</code></p><p><code class='latex inline'>\displaystyle y = \frac{4}{3}x -2 </code></p>
<p>Identify the x- and y-intercepts of each graph, if they exist.</p><img src="/qimages/22029" />
<p>Find an equation for a line with slope of <code class='latex inline'>\frac{2}{3}</code> that passes through the point `$(4, -1)$.</p>
<p>What is the slope of a line perpendicular to <code class='latex inline'>y=3x-2</code>?</p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>x=4</code></p><p><code class='latex inline'>y=-x+4</code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22040" />
<p>For safety reasons, a staircase should have a slope of between 0.58 and 0.70. Determine whether each staircase is within the safe range</p><img src="/qimages/1163" />
<p>You can find the equation of a line through two points even if one point is not the <code class='latex inline'>\displaystyle y </code>-intercept.</p> <ul> <li><p>Find the slope <code class='latex inline'>\displaystyle m </code> of the line passing through the two points.</p></li> <li><p>Using either point, substitute for <code class='latex inline'>\displaystyle x, y </code>, and <code class='latex inline'>\displaystyle m </code> into <code class='latex inline'>\displaystyle y=m x+b </code>.</p></li> <li><p>Solve for <code class='latex inline'>\displaystyle b </code> and rewrite <code class='latex inline'>\displaystyle y=m x+b </code> for the values of <code class='latex inline'>\displaystyle m </code> and <code class='latex inline'>\displaystyle b </code>. Write an equation in slope-intercept form for the line passing through each pair of points.</p></li> </ul> <p><code class='latex inline'>\displaystyle \begin{array}{lll}\text { a. }(2,5) \text { and }(6,7) & \text { b. }(-4,16) \text { and }(3,-5) & \text { c. }(-2,17) \text { and }(2,1)\end{array} </code></p>
<p>ABSTRACT REASONING Show that the equation of the line that passes through the points <code class='latex inline'>\displaystyle (0, b) </code> and <code class='latex inline'>\displaystyle (1, b+m) </code> is <code class='latex inline'>\displaystyle y=m x+b . </code> Explain how you can be sure that the point <code class='latex inline'>\displaystyle (-1, b-m) </code> also lies on the line.</p>
<p>Graph each equation.</p><p><code class='latex inline'>\displaystyle 3 x+5 y=12 </code></p>
<p>Slopes of roads are called grades and are expressed as percents.</p><p>(a) Calculate the grade of a road that rises 21 m over a run of 500 m.</p><p>(b) For a road to have a grade of 3%, how far does it have to rise over a run of 600 m?</p>
<p>If the intercepts of a line are <code class='latex inline'>\displaystyle (a, 0) </code> and <code class='latex inline'>\displaystyle (0, b) </code>, what is the slope of the line?</p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>3x-2y+6=0</code></p>
<p>Determine the equation of the line described by the given information.</p><p>parallel to <code class='latex inline'>y = 4x - 6</code>, passing through point (2, 6)</p>
<p>Identify the x- and y-intercepts of each graph.</p><img src="/qimages/22025" />
<p>For each line segment,</p> <ul> <li>count grid units to find the rise</li> <li>count grid units to find the run</li> <li>determine the slope</li> </ul> <img src="/qimages/1161" />
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle -\frac{1}{2} x-y=\frac{3}{4} </code></p>
<p>Determine the equation of the line described by the given information.</p><p>slope <code class='latex inline'>- \frac{2}{3}</code>, passing through the point <code class='latex inline'>(0, 6)</code>.</p>
<p>Find the slope of each line given the x- and y-intercepts, using the slope formula.</p><img src="/qimages/22042" />
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22034" />
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle -A x+B y=-C </code></p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><img src="/qimages/88462" />
<p>Write an equation for each transformation of <code class='latex inline'>\displaystyle y=x </code>.</p><p>vertical stretch by a factor of 2</p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>x+y=3</code></p><p><code class='latex inline'>x+y=2</code></p>
<p>Find an equation for a line that is perpendicular to <code class='latex inline'>2x - 3y + 6= 0</code> and has the same x-intercept as <code class='latex inline'>3x + 7y + 9 =0</code>.</p>
<p>Given a point <code class='latex inline'>A(-2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope is undefined</p>
<p>Railroad trains cannot go up tracks with a grade (slope) greater than 7%. To go over hills steeper than this, the railroad company builds switchbacks. How many switchbacks are needed to get to the top of a hill that is 250 m high? Assume that the maximum length of the run is 1 km. Explain your solution.</p><img src="/qimages/6878" />
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'>m = 2\dfrac{1}{2}, m= -\dfrac{2}{5}</code></p>
<p>ERROR ANALYSIS In Exercises 40 and 41 , describe and correct the error in graphing the function.</p><img src="/qimages/44103" />
<p>Determine the slope of each object.</p><img src="/qimages/132104" /><img src="/qimages/132105" />
<p>Find the slope of each line given the x- and y-intercepts, using the slope formula.</p><img src="/qimages/22043" />
<p>Write an equation for each line.</p><img src="/qimages/88428" />
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'> m = \dfrac{3}{4}, m = \dfrac{6}{8}</code></p>
<p>Write an equation for each line.</p><p><code class='latex inline'>\displaystyle m=3 </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,2) </code>.</p>
<p>For the line,</p> <ul> <li>identify the slope and the y-intercept.</li> <li>write the equation of the line in slope y-intercept form.</li> </ul> <img src="/qimages/10936" />
<p>The line contains the point <code class='latex inline'>\displaystyle (-4,-7) </code> and has the same slope as the graph of <code class='latex inline'>\displaystyle y+3=5(x+4) </code></p>
<p>For the line: </p> <ul> <li>identify the slope and the y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>x+y-3=0</code></p>
<p>Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.</p><p><code class='latex inline'>\displaystyle (3,-5),(-3,3),(0,2) </code></p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle -\frac{1}{3} x-\frac{2}{3} y=\frac{5}{3} </code></p>
<p>The slope and the y-intercept are given. Write the equation and graph each line.</p><p>slope= -<code class='latex inline'>\frac{2}{3}</code>, y-intercept= 2</p>
<p>A line segment has one endpoint of <code class='latex inline'>A(3, 1)</code>.</p><p><strong>(a)</strong> Plot the point A on a grid.</p><p><strong>(b)</strong> Use the slope <code class='latex inline'>\displaystyle{\frac{3}{2}}</code> to locate another possible endpoint B. What are the coordinates of point B? </p>
<p>Write an equation of each line in slope-intercept form.</p><p>slope <code class='latex inline'>\displaystyle -3 ; </code> through <code class='latex inline'>\displaystyle (1,-4) </code></p>
<p>Copy and complete the following table.The lines in the following table are parallel to the line 2r + 3y = 18.</p><p>a) Determine the x- and y-intercepts of the line 2x + 3y = 18.</p><p>b) Complete the following table.</p><img src="/qimages/22050" /><p>c) Describe how you can use intercepts to find a line that is parallel to a given line.</p>
<p> Find an equation for a line with a slope of <code class='latex inline'>\frac{2}{3}</code>, passing through <code class='latex inline'>(1, -4)</code>.</p>
<p>Write an equation for each line.</p><p><code class='latex inline'>\displaystyle m=0 </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,-2) . </code></p>
<p>Write an equation of the line with the given slope and <code class='latex inline'>\displaystyle y </code> -intercept.</p><p>slope: <code class='latex inline'>\displaystyle -3 </code></p><p><code class='latex inline'>\displaystyle y </code> -intercept: 0</p>
<p>Identify the slope and the y-intercept of each line.</p><p>a) <code class='latex inline'>\displaystyle y = -3x + 2 </code></p><p>b) <code class='latex inline'>\displaystyle y = \frac{3}{5}x -1 </code></p>
<p>a) What are the x and y intercepts of the line <code class='latex inline'>3x - y = 6</code>?</p><p>b) Graph the line.</p>
<p>Write an equation of each line.</p><p>slope <code class='latex inline'>\displaystyle =0 </code>; through <code class='latex inline'>\displaystyle (4,-2) </code></p>
<img src="/qimages/11023" /><p>What are the <code class='latex inline'>\displaystyle x </code> - and <code class='latex inline'>\displaystyle y </code>-intercepts of the line? A <code class='latex inline'>\displaystyle x </code>-intercept <code class='latex inline'>\displaystyle =2, y </code>-intercept <code class='latex inline'>\displaystyle =4 </code> B <code class='latex inline'>\displaystyle x </code>-intercept <code class='latex inline'>\displaystyle =-2, y </code>-intercept <code class='latex inline'>\displaystyle =-4 </code> C <code class='latex inline'>\displaystyle x </code>-intercept <code class='latex inline'>\displaystyle =-4, y </code>-intercept <code class='latex inline'>\displaystyle =2 </code> D <code class='latex inline'>\displaystyle x </code>-intercept <code class='latex inline'>\displaystyle =-4, y </code>-intercept <code class='latex inline'>\displaystyle =-2 </code></p>
<p>A ramp needs to have a slope of <code class='latex inline'>\displaystyle{\frac{3}{5}}</code>. </p><p>Determine the length of each vertical brace.</p><img src="/qimages/1165" />
<p>Write an equation of each line in slope-intercept form.</p><p>slope <code class='latex inline'>\displaystyle \frac{1}{2} ; </code> through <code class='latex inline'>\displaystyle (2,3) </code></p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>x+4y+3=0</code></p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=3x-2</code></p>
<p>CHALLENGE Write a function with an <code class='latex inline'>\displaystyle x </code>-intercept of <code class='latex inline'>\displaystyle (a, 0) </code> and a <code class='latex inline'>\displaystyle y </code>-intercept of <code class='latex inline'>\displaystyle (0, b) </code>.</p>
<p>Find an equation for the line containing line segment EF. </p><img src="/qimages/22748" />
<p>Write an equation of the line through each pair of points. Use point-slope form.</p><p><code class='latex inline'>\displaystyle \left(-\frac{1}{2},-\frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle (-3,-4) </code></p>
<p>Graph each equation using x- and y-intercepts.</p><p><code class='latex inline'>\displaystyle -4 x+y=-12 </code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22041" />
<p>Determine the slope of the sail on the toy sailboat.</p><img src="/qimages/144164" />
<p>The x-intercept is the x-coordinate of the point where a graph crosses the x-axis.</p><p><strong>(a)</strong> What is the value of the y-coordinate for any x-intercept? Use a diagram to explain your answer.</p><p><strong>(b)</strong> Find the x-intercept of each line.</p> <ul> <li><code class='latex inline'>y=3x - 6</code></li> <li><code class='latex inline'>y=\displaystyle{\frac{2}{3}}x + 5</code></li> </ul>
<p>Write an equation of each line.</p><p>slope <code class='latex inline'>\displaystyle =5 ; </code> through <code class='latex inline'>\displaystyle (0,2) </code></p>
<p>Write an equation of the line through each pair of points. Use point-slope form.</p><p><code class='latex inline'>\displaystyle \left(0, \frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle \left(\frac{5}{7}, 0\right) </code></p>
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (1,9) </code> and <code class='latex inline'>\displaystyle (6,2) </code></p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (0,0) </code> and <code class='latex inline'>\displaystyle (-1,-3) </code></p>
<p>Find the slope and y-intercept of each line.</p><img src="/qimages/22072" />
<p>Identify the x- and y-intercepts of each graph.</p><img src="/qimages/22026" />
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>2x+3y=12</code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>x=3</code></p><p><code class='latex inline'>x=0</code></p>
<p>Which line segment(s) are vertical? Which are horizontal? Explain how you know.</p><p><strong>a)</strong> <code class='latex inline'>A(2,6)</code> and <code class='latex inline'>B(5,2)</code></p><p><strong>b)</strong> <code class='latex inline'>C(-3,4)</code> and <code class='latex inline'>D(3,2)</code></p>
<p>The slope and the y-intercept are given. Write the equation and graph each line.</p><p>slope= undefined, y-intercept= none, x-intercept= 3</p>
<p>Write an equation of the line through each pair of points. Use point-slope form.</p><p><code class='latex inline'>\displaystyle \left(\frac{3}{2},-\frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle \left(-\frac{2}{3}, \frac{1}{3}\right) </code></p>
<p>The slope and the y-intercept are given. Write the equation and graph each line.</p> <ul> <li>slope = 0</li> <li>y-intercept: -4</li> </ul>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y=4.2 x+7.9 </code></p>
<p>Reflect the given graph on the x-axis.</p><img src="/qimages/5233" />
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (-5,4) </code> and <code class='latex inline'>\displaystyle (-2,-1) </code></p>
<p>Given a point <code class='latex inline'>A(-2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope = <code class='latex inline'>-3</code></p>
<p>Write the equation for each line. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle m=-\frac{3}{8} </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,12) </code></p>
<p>Write an equation of the line with the given slope and <code class='latex inline'>\displaystyle y </code> -intercept. </p><p>slope: 0</p><p><code class='latex inline'>\displaystyle y </code> -intercept: 5</p>
<p>A hiking trail has been cut diagonally along the side of a hill, as shown. What is the slope of the trail?</p><img src="/qimages/1169" />
<p>The line <code class='latex inline'> A x+B y=8 </code> passes through the points <code class='latex inline'> (2,1) </code> and <code class='latex inline'> (4,-2) </code> . Find the values of <code class='latex inline'> A </code> and <code class='latex inline'> B </code> .</p>
<p>For each line segment,</p> <ul> <li>count grid units to find the rise</li> <li>count grid units to find the run</li> <li>determine the slope</li> </ul> <img src="/qimages/1160" />
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22039" />
<p>Find the slope of each line given the x- and y-intercepts, using the slope formula.</p><img src="/qimages/22044" />
<p>Write an equation of the line with the given slope and <code class='latex inline'>\displaystyle y </code> -intercept.</p><p>slope: <code class='latex inline'>\displaystyle -7 </code></p><p><code class='latex inline'>\displaystyle y </code> -intercept: 1</p>
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'>m=5, m=-5</code></p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><img src="/qimages/88464" />
<p>Write an equation of each line.</p><p>slope <code class='latex inline'>\displaystyle =\frac{5}{6} ; </code> through <code class='latex inline'>\displaystyle (22,12) </code></p>
<p>Find the <code class='latex inline'>\displaystyle x </code> - and <code class='latex inline'>\displaystyle y </code> -intercepts of the graph of each linear function. Describe what the intercepts mean.</p><img src="/qimages/39110" />
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24682" />
<p>Write an equation for each line.</p><p><code class='latex inline'>\displaystyle m=-5 </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,-7) . </code></p>
<p>Classify each pair of lines as parallel, perpendicular, or neither. Explain.</p><p><code class='latex inline'>y =3, x = -2</code></p>
<p>To be safe, a wheelchair ramp needs to have a slope no greater than 0.08. Does a wheelchair ramp with a vertical rise of 1.4 m along a horizontal run of 8 m satisfy the safety regulation? </p>
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24679" />
<p>Classify each pair of lines as parallel, perpendicular, or neither. Explain.</p><p><code class='latex inline'>y = -3x + 2</code></p><p><code class='latex inline'>\displaystyle y = -3x -8 </code></p>
<p>a) Write the line <code class='latex inline'>5x-2y+4=0</code> in the form <code class='latex inline'>y=mx+b</code>. </p><p>b) State the slope of the line <code class='latex inline'>5x-2y+4=0</code>. </p><p>c) State the slope of a line that is perpendicular to the lines <code class='latex inline'>5x-2y+4=0</code>. </p><p>d) Write the equations of two lines that are perpendicular to the line <code class='latex inline'>5x-2y+4=0</code>. </p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'> x+y-4=0</code></p>
<p>Write an equation of each line.</p><p>slope =3, through (1,5)</p>
<p>Find the slope and y-intercept of each line.</p><img src="/qimages/22070" />
<p>Temperature The relation between degrees Fahrenheit <code class='latex inline'>\displaystyle F </code> and degrees Celsius <code class='latex inline'>\displaystyle C </code> is described by the function <code class='latex inline'>\displaystyle F=\frac{9}{5} C+32 . </code> In the following ordered pairs, the first element is degrees Celsius and the second element is its equivalent in degrees Fahrenheit. Find the unknown measure in each ordered pair. <code class='latex inline'>\displaystyle \begin{array}{llll}\text { a. }(43, m) & \text { b. }(-12, n) & \text { c. }(p, 12) & \text { d. }(q, 19)\end{array} </code></p>
<p>Find the slope of each line given the x- and y-intercepts, using the slope formula.</p><img src="/qimages/22045" />
<p>What is the slope of a line that is parallel to each line?</p><p> <code class='latex inline'>5x-3y-15=0</code></p>
<p> In 1967, Montreal hosted Expo 67, an international fair, to celebrate Canada’s 100th birthday. Canada’s pavilion was an upside-down pyramid called Katimavik, which means meeting place in Inuktitut, the language of the Inuit. The base width is about 55 m and the height is about 18 m. Calculate the slope of the sides. </p>
<p>For the line: </p> <ul> <li>identify the slope and the y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>3x+2y-5=0</code></p>
<p>Given a point <code class='latex inline'>A(-2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope = 4</p>
<p>Geometry Graph <code class='latex inline'>\displaystyle x+4 y=8,4 x-y=-1, x+4 y=-12 </code>, and <code class='latex inline'>\displaystyle 4 x-y=20 </code> in the same coordinate plane. What figure do the four lines appear to form?</p>
<p>Find the slope of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle \left(0,-\frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle \left(\frac{7}{5}, 10\right) </code></p>
<p>Identify the slope and the y-intercept of the line.</p><img src="/qimages/6663" />
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (2,7) </code> and <code class='latex inline'>\displaystyle (-3,11) </code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22037" />
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (-3,5) </code> and <code class='latex inline'>\displaystyle (4,5) </code></p>
<p>ERROR ANALYSIS Describe and correct the error in writing an equation of the line with a slope of 2 and a <code class='latex inline'>\displaystyle y </code> -intercept of <code class='latex inline'>\displaystyle 7 . </code> <code class='latex inline'>\displaystyle y=7 x+2 </code></p>
<p>State the slope and the y-intercept of each line, if they exist.</p><p><code class='latex inline'>y=-5</code></p>
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (-10,3) </code> and <code class='latex inline'>\displaystyle (-2,-5) </code></p>
<p>They-intercept is the y-coordinate of the point where a graph crosses the y-axis. The value of the x-coordinate for any y-intercept is 0. The x-intercept is the x-coordinate of the point where a graph crosses the x-axis. The value of the y-coordinate for any intercept is 0. Find the x-intercept and the y-intercept of each line.</p><p><code class='latex inline'>y=2x-6</code></p>
<p>a) Rearrange <code class='latex inline'>\displaystyle 3 x-4 y+8=0 </code> into the form <code class='latex inline'>\displaystyle y=m x+b </code></p><p>b) Identify the slope and the <code class='latex inline'>\displaystyle y </code>-intercept.</p><p>c) Use this information to graph the line.</p>
<p>Calculate the slope of each line segment, where possible.</p><img src="/qimages/144167" /><p><code class='latex inline'>CD</code></p>
<p>Write a linear function <code class='latex inline'>\displaystyle f </code> with the given values. </p><p><code class='latex inline'>\displaystyle f(0)=2, f(2)=4 </code></p>
<p>Write the equation of the line through each point. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle (-7,10) ; </code> parallel to <code class='latex inline'>\displaystyle 2 x-3 y=-3 </code></p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y=-\frac{3}{5} x+3 </code></p>
<p>Roofers call the slope of a roof its pitch. Roofs have different pitch classifications, which indicate how safe they are for roofers to walk on. They are classified as shown in this table</p><img src="/qimages/1166" /> <ul> <li>A roof is 10 m wide and has a pitch of <code class='latex inline'>\displaystyle{\frac{5}{12}}</code>. Find the height.</li> </ul>
<p>Determine the equation of the line described by the given information.</p><p>passing through points (2, 7) and (6, 11).</p>
<p>Identify the x- and y-intercepts of each graph.</p><img src="/qimages/22027" />
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22032" />
<img src="/qimages/10942" /><p>Find the slope of each line segment.</p><p>a) <code class='latex inline'>\displaystyle \mathrm{AB} </code></p><p>c) <code class='latex inline'>\displaystyle \mathrm{EF} </code></p><p>b) <code class='latex inline'>\displaystyle \mathrm{CD} </code></p><p>d) <code class='latex inline'>\displaystyle \mathrm{GH} </code></p>
<p>Find the area of the polygon with the given vertices. </p><p><code class='latex inline'>J(-3,4), K(4,4), L(3,-3)</code></p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>2x+5y+10=0</code></p>
<p>Determine the equation of the line described by the given information.</p><p>perpendicular to <code class='latex inline'>y = -5x + 3</code>, passing through point <code class='latex inline'>(-1, -2)</code>.</p>
<p>Write an equation for each line. Then graph the line.</p><p><code class='latex inline'>\displaystyle m=0 </code>, through <code class='latex inline'>\displaystyle (5,-1) </code></p>
<p>Find the intercepts and graph each line.</p><p><code class='latex inline'>\displaystyle -3 x+2 y=6 </code></p>
<p>State the equation and sketch the graph of each line described below.</p><p>passing through <code class='latex inline'>(5, 6)</code>, and <code class='latex inline'>(5, -9)</code></p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (0,0) </code> and <code class='latex inline'>\displaystyle (3,4) </code></p>
<p>Find the area of the polygon with the given vertices. </p><p><code class='latex inline'>E(3,1), F(3,-2), G(-2,-2)</code></p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=\frac{3}{4}x-5</code></p>
<p>Write an equation for each line.</p><p><code class='latex inline'>\displaystyle m=\frac{5}{6} </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,12) </code></p>
<p>For the line,</p> <ul> <li>identify the slope and the y-intercept.</li> <li>write the equation of the line in slope y-intercept form.</li> </ul> <img src="/qimages/10937" />
<p>Write each equation in slope-intercept form. <code class='latex inline'>\displaystyle -4 x+3 y=1 </code></p>
<p>What is the slope of a line parallel to <code class='latex inline'>y=3x-2</code>?</p>
<p>Vocabulary What is a <code class='latex inline'>\displaystyle y </code>-intercept? How is a <code class='latex inline'>\displaystyle y </code>-intercept different from an <code class='latex inline'>\displaystyle x </code>-intercept?</p>
<p>Determine the slope of a line perpendicular to each of the following:</p><p><strong>(a)</strong> <code class='latex inline'>y = 3x -5</code></p><p><strong>(b)</strong> <code class='latex inline'>13x - 7y - 11 = 0</code></p>
<p>Write each equation in slope-intercept form. Then find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle y=7 </code></p>
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (-m, n),(3 m,-n) </code></p>
<p>Write the equation of the line through each point. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle (-3,1) ; </code> perpendicular to <code class='latex inline'>\displaystyle y=-\frac{2}{5} x-4 </code></p>
<p>What is the slope of the line <code class='latex inline'>y=3x-2</code>?</p>
<p>State the equation and sketch the graph of each line described below.</p><p>having slope 8 and y-intercept 6</p>
<p>Which line is parallel to the line <code class='latex inline'>y = \frac{1}{5}x -1</code>?</p><p>A. <code class='latex inline'>y = - \frac{1}{5}x -1</code></p><p>B. <code class='latex inline'>y = \frac{1}{5}x + 3</code></p><p>C. <code class='latex inline'>y = 5x + 1</code></p><p>D. <code class='latex inline'>y = -5x -4</code></p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (-1,4) </code> and <code class='latex inline'>\displaystyle (1,7) </code></p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=2x-\frac{1}{3}</code></p>
<p>Write the equation of each line in question 7.</p>
<p>Find the slope and y-intercept of each line.</p><img src="/qimages/22069" />
<p>Given a point <code class='latex inline'>A(-2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope = <code class='latex inline'>\displaystyle{\frac{2}{3}}</code></p>
<p> Determine the x- and y-intercepts of each line. Then, graph the line.</p><p><code class='latex inline'>\displaystyle 6x - y = 9 </code></p>
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'>m=0, m=undefined</code></p>
<p>The <code class='latex inline'>\displaystyle x </code> - and <code class='latex inline'>\displaystyle y </code> -intercepts of the graph of the equation <code class='latex inline'>\displaystyle 3 x+5 y=k </code> are integers. Describe the values of <code class='latex inline'>\displaystyle k </code>. Explain your reasoning.</p>
<p>Determine the slope of each object.</p><img src="/qimages/1158" />
<p>a. Write the point-slope form of the line that passes through <code class='latex inline'>\displaystyle A(-3,12) </code> and <code class='latex inline'>\displaystyle B(9,-4) . </code> Use point <code class='latex inline'>\displaystyle A </code> in the equation.</p><p>b. Write the point-slope form of the same line using point <code class='latex inline'>\displaystyle B </code> in the equation.</p><p>c. Rewrite each equation in standard form. What do you notice?</p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (2,1) </code> and <code class='latex inline'>\displaystyle (2,6) </code></p>
<p>Explain how the slopes of perpendicular lines are related. Create an example to support your explanation.</p>
<p>What is the slope of the line at the right?</p><img src="/qimages/56654" />
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (0,4) </code> and <code class='latex inline'>\displaystyle (2,0) </code></p>
<p>Find the slope and y-intercept of each line.</p><img src="/qimages/22071" />
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>a) <code class='latex inline'> 3x + 4y = 12</code></p>
<p>Write the coordinates of points <code class='latex inline'>B</code> and <code class='latex inline'>D</code>.</p><img src="/qimages/633" />
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22036" />
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (1,0) </code> and <code class='latex inline'>\displaystyle (5,5) </code></p>
<p>For the line: </p> <ul> <li>identify the slope and the y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>x - 4y + 12=0</code></p>
<p>The Great Pyramid of Cheops has a height of about 147 m and a base width of about 230 m. How does its slope compare to a standard staircase with slope 0.7?</p>
<p>In Exercises 9-12, write an equation of the line in slope-intercept form. (See Example 2.)</p><img src="/qimages/44381" />
<p>Calculate the slope of each line segment, where possible.</p><img src="/qimages/1162" /><p>(a) AB</p><p>(b) CD</p><p>(c) EF</p><p>(d) GH</p><p>(e) IJ</p><p>(f) KL</p>
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>y=\dfrac{2}{3}x + 4</code></p>
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (-2,-5),(-7,10) </code></p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y=-7 x-9 </code></p>
<p>For each linear relation in question 1, </p> <ul> <li>identify the slope and y-intercept</li> <li>use this information to graph the line</li> </ul> <p><code class='latex inline'>x-3y-8=0</code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (0,0) </code> and <code class='latex inline'>\displaystyle (2,6) </code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>x+y-2=0</code></p><p><code class='latex inline'>x-y-2=0</code></p>
<p>Write each equation in slope-intercept form. <code class='latex inline'>\displaystyle x-2 y+3=1 </code></p>
<p>Which are the slope and the <code class='latex inline'>\displaystyle y </code>-intercept of the line <code class='latex inline'>\displaystyle y=-3 x-1 ? </code> </p><p>A <code class='latex inline'>\displaystyle m=3, b=1 </code></p><p>B <code class='latex inline'>\displaystyle m=-3, b=1 </code></p><p>C <code class='latex inline'>\displaystyle m=-3, b=-1 </code></p><p>D <code class='latex inline'>\displaystyle m=\frac{1}{3}, b=-1 </code></p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y=\frac{1}{2} x-2 </code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=2</code></p><p><code class='latex inline'>y=x</code></p>
<p>Graph each equation.</p><p><code class='latex inline'>\displaystyle 3 y-x=-6 </code></p>
<p>State the slope and the y-intercept of each line, if they exist.</p><p><code class='latex inline'>x=1</code></p>
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24680" />
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24678" />
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (8,-1) </code> and <code class='latex inline'>\displaystyle (4,-4) </code></p>
<p>Write the equation for each line. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle m=\frac{1}{2} </code> and the <code class='latex inline'>\displaystyle y </code>-intercept is <code class='latex inline'>\displaystyle (0,0) . </code></p>
<p>Find the slope of the line that passes through the two points.</p><p><code class='latex inline'>\displaystyle (1,3) </code> and <code class='latex inline'>\displaystyle (4,9) </code></p>
<p>Draw a graph and determine the slope of each line using the rise and run from the graph.</p><img src="/qimages/22038" />
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24681" />
<p>Write in point-slope form an equation of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle (7,11) </code> and <code class='latex inline'>\displaystyle (13,17) </code></p>
<p>Identify the slope and the y-intercept of the line.</p><img src="/qimages/6662" />
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>c) <code class='latex inline'>x-3y = 6</code></p>
<p>Identify the x- and y-intercepts of each graph, if they exist.</p><img src="/qimages/22028" />
<p>Find the slope of the line that passes through each pair of points.</p><p><code class='latex inline'>\displaystyle (-1,4),(3,-8) </code></p>
<p>Write an equation for each transformation of <code class='latex inline'>\displaystyle y=x </code>.</p><p>vertical stretch by a factor of 4</p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><p><code class='latex inline'>\displaystyle x=-3 </code></p>
<p>Graph each equation.</p><p><code class='latex inline'>\displaystyle y+3=3 </code></p>
<p>State the equation and sketch the graph of each line described below.</p><p>having x-intercept 5 and y-intercept -3</p>
<p>For safety reasons, a staircase should have a slope of between 0.58 and 0.70. Determine whether each staircase is within the safe range</p><img src="/qimages/1164" />
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>y=4</code></p>
<p>The x-intercept of a line is <code class='latex inline'>p</code>, and the y-intercept is <code class='latex inline'>q</code>. Write an equation of the line.</p>
<p>Find the slope of each line given the x- and y-intercepts, using the slope formula.</p><img src="/qimages/22046" />
<p>What is the slope of the line passing through the following point? <code class='latex inline'>\displaystyle (-1,-3) </code> and <code class='latex inline'>\displaystyle (3,1) </code></p>
<p>Write the equation of the line through each point. Use slope-intercept form.</p><p><code class='latex inline'>\displaystyle (1,-1) ; </code> parallel to <code class='latex inline'>\displaystyle y=\frac{2}{5} x-3 </code></p>
<p>For safety reasons, an extension ladder should have a slope of between 6.3 and 9.5 when it is placed against a wall. If a ladder reaches 8 m up a wall, what are the maximum and minimum distances from the foot of the ladder to the wall?</p>
<p>Find the equation of the line which passes through the following points:</p><p><code class='latex inline'>\displaystyle (3, 2) </code> and <code class='latex inline'>\displaystyle (6, 3) </code></p>
<p>Find the slope and the y-intercept of each line.</p><p> <img src="/qimages/22076" /></p>
<p>A section of road is built with a vertical rise of 2.5 m over a horizontal run of 152 m. Find the slope, to the nearest hundredth.</p>
<p>Two ramps are being built with the same slope. The first ramp is twice the height of the second ramp. Does the first ramp have to be twice as long as the second ramp? Explain. </p>
<p>Find the slope of the line passing through each of the following pairs of points. </p><p><code class='latex inline'>\displaystyle (3,5) </code> and <code class='latex inline'>\displaystyle (6,5) </code></p>
<p>Write the equation of a line with the given slope and y-intercept. Then, graph the line.</p><p><code class='latex inline'>m = \frac{2}{3}, b = -4</code></p>
<p>What is the slope of a line that is parallel to each line?</p><p> <code class='latex inline'>y=-2x+3</code></p>
<p>Given a point <code class='latex inline'>A(-2, 5)</code>, find the coordinates of a point B so that the line segment AB has each slope.</p><p>slope = 0</p>
<p>Roofers call the slope of a roof its pitch. Roofs have different pitch classifications, which indicate how safe they are for roofers to walk on. They are classified as shown in this table</p><img src="/qimages/1166" /><p>(a) Classify each roof by its pitch.</p><img src="/qimages/1167" /><img src="/qimages/1168" />
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>d) <code class='latex inline'> -2x+3y = 6</code></p>
<p>Determine the equation of the quadratic curve of best fit for the data.</p><img src="/qimages/2489" />
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=-\frac{2}{5}x</code></p>
<p>Find the intercepts and graph each line.</p><p><code class='latex inline'>\displaystyle 2 x+5 y=-10 </code></p>
<p>Find the slope of the line through each pair of points. <code class='latex inline'>\displaystyle (-2,-1) </code> and <code class='latex inline'>\displaystyle (8,-3) </code></p>
<p>ERROR ANALYSIS In Exercises 40 and 41 , describe and correct the error in graphing the function.</p><img src="/qimages/44104" />
<p>Write the equation of each line in question 2.</p>
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=3x+1</code></p><p><code class='latex inline'>y=\dfrac{1}{3}x+1</code></p>
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>y = -\dfrac{2}{5}x-7</code></p>
<p>a) Write the line <code class='latex inline'>3x+2y-7=0</code> in the form <code class='latex inline'>y=mx+b</code>.</p><p>b) State the slope of the line <code class='latex inline'>3x+2y-7=0</code>. </p><p>c) State the slope of a line parallel to the line <code class='latex inline'>3x+2y-7=0</code>. </p><p>d) Write the equations of two lines that are parallel to the line <code class='latex inline'>3x+2y-7=0</code>. </p>
<p>The slope and the y-intercept are given. Write the equation and graph each line.</p><p>slope= 0, y-intercept= -2</p>
<p>Write an absolute value equation for each graph.</p><img src="/qimages/89595" />
<p>Error Analysis A classmate says that the graph of <code class='latex inline'>\displaystyle 3 y-2 x=5 </code> has a slope of <code class='latex inline'>\displaystyle 2 . </code> What mistake did he make?</p>
<p>A steel beam goes between the tops of two buildings that are 7 m apart. One building is 41 m tall. The other is 52 m tall. What is the slope of the beam?</p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=-2x+4</code></p>
<p>Graph each pair of lines on the same coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=2x+3</code></p><p><code class='latex inline'>y=2x-1</code></p>
<p>They-intercept is the y-coordinate of the point where a graph crosses the y-axis. The value of the x-coordinate for any y-intercept is O. The x-intercept is the x-coordinate of the point where a graph crosses the x—axis. The value of the y-coordinate for any intercept is 0. Find the x-intercept and the y-intercept of each line.</p><p><code class='latex inline'>y=\frac{2}{5}x+4</code></p>
<p>Calculate the slope of each line segment, where possible.</p><img src="/qimages/144167" /><p><code class='latex inline'>EF</code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>2x+y-1=0</code></p><p><code class='latex inline'>\dfrac{1}{2}x+y-2=0</code></p>
<p>Identify the x- and y-intercepts of each graph, if they exist.</p><img src="/qimages/22030" />
<p>Determine the x- and y-intercepts and use them to graph each line. </p><p>f) <code class='latex inline'>4y=8</code></p>
<p>What is the slope of a line that is parallel to each line?</p><p><code class='latex inline'>x=3</code></p>
<p>Find the equation of the line which passes through the following points:</p><p><code class='latex inline'>\displaystyle (-2, 3) </code> and <code class='latex inline'>\displaystyle (1, -3) </code></p>
<p>What are the intercepts of <code class='latex inline'>\displaystyle 3 x+y=6 ? </code> Graph the equation.</p>
<p>Find ordered pair is that is on this line.</p><p><code class='latex inline'> y = 5x - 1</code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=3</code></p><p><code class='latex inline'>y=-2</code></p>
<p>Find an equation for a line passing through the point <code class='latex inline'>(-3, -4)</code> and <code class='latex inline'>(6, 8)</code>.</p>
<p>Find an equation for a line parallel to <code class='latex inline'>3x - 4y = 12</code>, with an x-intercept of <code class='latex inline'>6</code>.</p>
<p>Which line is perpendicular to the line <code class='latex inline'>y = \frac{3}{2}x -1</code>?</p><p>A. <code class='latex inline'>y = \frac{2}{3}x + 1</code></p><p>B. <code class='latex inline'>y = - \frac{2}{3}x +4</code></p><p>C. <code class='latex inline'>y = \frac{3}{2}x -3</code></p><p>D. <code class='latex inline'>y = -\frac{3}{2}x -1</code></p>
<p>In the graph at the right, (0, 1) and (4, 3) lie on the line. Which ordered pair also lies on the line?</p><img src="/qimages/24645" /><p>A. (1, 1)</p><p>B. (2, 2)</p><p>C. (3, 3)</p><p>D. (4, 4)</p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>y=5</code></p>
<p>Error Analysis Your friend says the line <code class='latex inline'>\displaystyle y=-2 x+3 </code> is perpendicular to the line <code class='latex inline'>\displaystyle x+2 y=8 </code>. Do you agree? Explain.</p>
<p>Write an equation of each line.</p><p>slope <code class='latex inline'>\displaystyle =-\frac{3}{5} ; </code> through <code class='latex inline'>\displaystyle (-4,0) </code></p>
<p>Find the slope and <code class='latex inline'>\displaystyle y </code>-intercept of each line.</p><img src="/qimages/88463" />
<p>The slopes of the two lines are given. Conclude whether the lines are parallel, perpendicular, or neither. Justify your answers. </p><p><code class='latex inline'> m= 3, m= -\dfrac{1}{3}</code></p>
<p>Graph each pair of lines on the coordinate grid. Find their slopes and conclude whether the lines are parallel, perpendicular, or neither. </p><p><code class='latex inline'>y=1</code></p><p><code class='latex inline'>x=-1</code></p>
<p>Find the slope of the line through each pair of points.</p><p><code class='latex inline'>\displaystyle \left(\frac{3}{2},-\frac{1}{2}\right) </code> and <code class='latex inline'>\displaystyle \left(-\frac{2}{3}, \frac{1}{3}\right) </code></p>
<p>Classify each pair of lines as parallel, perpendicular, or neither. Explain.</p><p><code class='latex inline'>y = 2x + 5</code></p><p><code class='latex inline'>\displaystyle y = - \frac{1}{2}x -2 </code></p>
<p>Write an equation of the line with the given slope and <code class='latex inline'>\displaystyle y </code> -intercept. </p><p>slope: 2</p><p><code class='latex inline'>\displaystyle y </code> -intercept: 9</p>
<p>A line segment has one endpoint of <code class='latex inline'>\displaystyle \mathrm{A}(6,-2) </code> and slope of <code class='latex inline'>\displaystyle -\frac{3}{4} </code>. Find the coordinates of another possible endpoint B by adding the appropriate values to the coordinates of point <code class='latex inline'>\displaystyle A </code>.</p>
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