4. Q4a
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Similar Question 1
<p>Determine whether each equation is a linear equation. If so, write the equation in standard form.</p><p><code class='latex inline'>2y=y+2x-3</code></p>
Similar Question 2
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>5x+4y=8</code> for x ={-􏰸4, -􏰸1, 0, 2, 4, 6}</p>
Similar Question 3
<p>Banquet hall charges according to the equation <code class='latex inline'> 40n - C + 250 = 0 </code>.</p> <ul> <li>Express the equation in slope y-intercept form: <code class='latex inline'>C=mn+b</code>.</li> </ul>
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>Determine whether each equation is a linear equation. If so, write the equation in standard form.</p><p><code class='latex inline'>y-8=10-x</code></p>
<p>Rewrite each equation in the form <code class='latex inline'>y = mx + b</code></p><p><code class='latex inline'>3x + 5y + 15 = 0</code></p>
<p>Write three equations equivalent to each of the following equations.</p><p><code class='latex inline'>\displaystyle 2 x+y=7 </code></p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y = 7x + 0.4 </code></p>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have fraction in them.</p><p><code class='latex inline'>\displaystyle -\frac{2}{5}x - \frac{1}{5}y = -1 </code></p>
<p>Write two equivalent equations for each.</p><p><code class='latex inline'> y = \dfrac{2}{3}x + 5</code></p>
<p>You can change an equation from slope y-intercept form to standard form by rearranging terms in the equation. Rearrange each of the following equations into standard form, <code class='latex inline'>Ax+By+C=0</code>, and identify the coefficients <code class='latex inline'>A, B,</code> and <code class='latex inline'>C</code>.</p><p><code class='latex inline'>y=x - 3</code></p>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have fraction in them.</p><p><code class='latex inline'>\displaystyle \frac{-2}{3}x + \frac{2}{3}y + \frac{1}{4} = 0 </code></p>
<p>Express each equation in the from <code class='latex inline'>y=mx + b</code>.</p><p><code class='latex inline'>3x+2y-5=0</code></p>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have a fraction in them.</p><p><code class='latex inline'>\displaystyle \frac{2}{3}x + \frac{2}{5}y + 2 = -1 </code></p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y = 1.2x -0.5 </code></p>
<p>a) Multiply both sides of the equation <code class='latex inline'> x+y=6 </code> by <code class='latex inline'> -3 </code> .</p><p>b) Do the ordered pairs you found in question 1 satisfy the new equation?</p>
<p>Write each equation in standard form using integers.</p><p>y = 2x + 5</p>
<p>Write each equation in standard form. Identify <code class='latex inline'>\displaystyle A, B </code>, and <code class='latex inline'>\displaystyle C </code>.</p><p><code class='latex inline'>\displaystyle -8 x=9 y-6 </code></p>
<p>Write each equation in standard form. Identify <code class='latex inline'>\displaystyle A, B </code>, and <code class='latex inline'>\displaystyle C </code>.</p><p><code class='latex inline'>\displaystyle \frac{x+5}{3}=-2 y+4 </code></p>
<p>Change the following equation of lines to the y-intercept form of the line. State the slope and the y-intercept for each.</p><p><code class='latex inline'>\displaystyle \frac{2}{3}x + y + \frac{1}{4} = 0 </code></p>
<p>Two parabolas have the same x-intercepts, at <code class='latex inline'>(0, 0)</code> and <code class='latex inline'>(10, 0)</code>. One parabola has a maximum value of 2. The other parabola has a minimum value of <code class='latex inline'>-4</code>. Sketch the graphs of the parabolas on the same axes.</p>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have fraction in them.</p><p><code class='latex inline'>\displaystyle -\frac{1}{12}x - \frac{5}{3}y + \frac{1}{3} = \frac{1}{10} </code></p>
<p>State the slope of a line that is perpendicular to the line represented by each function.</p><p>a) <code class='latex inline'>\displaystyle y = 2x + 9 </code></p><p>b) <code class='latex inline'>\displaystyle y = -5x -3 </code></p><p>c) <code class='latex inline'>\displaystyle \frac{2}{3}x - y + 3 = 9 </code></p><p>d) <code class='latex inline'>\displaystyle y = 26 </code></p><p>e) <code class='latex inline'>\displaystyle y = x </code></p><p>f) <code class='latex inline'>\displaystyle x = - 3 </code></p>
<p>You can change an equation from slope y-intercept form to standard form by rearranging terms in the equation. Rearrange each of the following equations into standard form, <code class='latex inline'>Ax + By + C=0</code>, and identify the coefficients <code class='latex inline'>A, B,</code> and <code class='latex inline'>C</code>.</p><p><code class='latex inline'>y=-2x+7</code></p>
<p>Write two equivalent equations for each.</p><p><code class='latex inline'> y = 5x -3</code></p>
<p>Explain how you can determine whether a point at (x, y) is above, below, or on the line given by <code class='latex inline'>2x-y=8</code> without graphing it. Give an example of each.</p>
<p>Write three equations equivalent to each of the following equations.</p><p><code class='latex inline'>\displaystyle y=4 x-3 </code></p>
<p>Write two equivalent equations for each.</p><p><code class='latex inline'> 4x +3y = 12</code></p>
<p>Write each equation in standard form. Identify <code class='latex inline'>\displaystyle A, B </code>, and <code class='latex inline'>\displaystyle C </code>.</p><p><code class='latex inline'>\displaystyle 3 x=-2 y-1 </code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>\frac{1}{2}x+y=2</code> for x= {􏰸-4, 􏰸-1, 1, 4, 7, 8}</p>
<p>a) Multiply both sides of the equation <code class='latex inline'> x+y=6 </code> by 2 .</p><p>b) Do the ordered pairs you found in question 1 satisfy the new equation?</p>
<p>Write an equation of each line in standard form with integer coefficients.</p><p><code class='latex inline'>\displaystyle y = - \frac{3}{7}x +4 </code></p>
<p> Write three equations equivalent to each of the following equations.</p><p> <code class='latex inline'> x-y=4 </code> </p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>2x - 5y + 8=0</code></p>
<p>Which two of the following linear equations will have the same graph?</p><p>a) <code class='latex inline'> 2y = \dfrac{1}{2}x+4</code></p><p>b) <code class='latex inline'>y=\dfrac{1}{4}x +1</code></p><p>c) <code class='latex inline'>4y = x+4</code></p>
<p>If <code class='latex inline'> y = 4x-5</code> and <code class='latex inline'>5y=kx-25</code> are equivalent linear equations, what is the value of <code class='latex inline'>k</code>?</p>
<p>Determine whether each equation is a linear equation. If so, write the equation in standard form.</p><p><code class='latex inline'>2y=y+2x-3</code></p>
<p>Identify the slope and the y-intercept of each line.</p><p><code class='latex inline'>x + 3y - 3=0</code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>y=3x-1</code> for x 􏰻={􏰸-5, -􏰸2, 1, 3, 4}</p>
<p>Express each equation in the from <code class='latex inline'>y=mx + b</code>.</p><p><code class='latex inline'>2x + 3y + 6=0</code></p>
<p>Are the three equations from questions 1,2, and 3 equivalent? Explain.</p>
<p>If <code class='latex inline'>y =6x+2</code> and <code class='latex inline'>4y=24x +k</code> are equivalent linear equations, what is the value of <code class='latex inline'>k</code>?</p>
<p>Write two equivalent equations for each.</p><p><code class='latex inline'> x+y = 7</code></p>
<p>Express each equation in the from <code class='latex inline'>y=mx + b</code>.</p><p><code class='latex inline'>x-4y+12=0</code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>3x-2y=5</code> for x= {􏰸-3, -􏰸1, 2, 4, 5}</p>
<p>Banquet hall charges according to the equation <code class='latex inline'> 40n - C + 250 = 0 </code>.</p> <ul> <li>Express the equation in slope y-intercept form: <code class='latex inline'>C=mn+b</code>.</li> </ul>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have fraction in them.</p><p><code class='latex inline'>\displaystyle \frac{11}{12}x + \frac{5}{4}y + \frac{1}{4} = 0 </code></p>
<p>Which is <em>not</em> an equivalent equation for <code class='latex inline'> 6x+3y = 15</code></p><p>a) <code class='latex inline'>2x+y = 5</code></p><p>b) <code class='latex inline'>12x +6y = 30</code></p><p>c) <code class='latex inline'>9x +6y = 18</code></p><p>d) <code class='latex inline'>x+\dfrac{1}{2}y = \dfrac{5}{2}</code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>y=\frac{1}{4}x-3</code> for x ={􏰸4, 􏰸2, 0, 2, 4, 6}</p>
<p>Write each equation in standard form. Identify <code class='latex inline'>\displaystyle A, B </code>, and <code class='latex inline'>\displaystyle C </code>.</p><p><code class='latex inline'>\displaystyle y=-4 x-7 </code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>5x+4y=8</code> for x ={-􏰸4, -􏰸1, 0, 2, 4, 6}</p>
<p>Write three equations equivalent to each of the following equations.</p><p><code class='latex inline'>\displaystyle x+y=2 </code></p>
<p>Consider the linear functions <code class='latex inline'>f(x) = ax + b</code> and <code class='latex inline'>g(x) = cx + d</code>. Suppose that <code class='latex inline'>f(2) = g(2)</code> and <code class='latex inline'>f(5) = g(5)</code>.</p><p>Show that the functions must be equivalent.</p>
<p>Write each equation in standard form. Identify <code class='latex inline'>\displaystyle A, B </code>, and <code class='latex inline'>\displaystyle C </code>.</p><p><code class='latex inline'>\displaystyle 12 y=4 x+8 </code></p>
<p>Rewrite each equation in the form <code class='latex inline'>y = mx + b</code></p><p><code class='latex inline'>2x + y -6 = 0</code></p>
<p>You can change an equation from slope y-intercept form to standard form by rearranging terms in the equation. Rearrange each of the following equations into standard form, <code class='latex inline'>Ax+By+C=0</code>, and identify the coefficients <code class='latex inline'>A, B,</code> and <code class='latex inline'>C</code>.</p><p><code class='latex inline'>y=\displaystyle{\frac{3}{4}}x-2</code></p>
<p>Sketch the graph clearly showing x and y-intercepts.</p><p><code class='latex inline'>\displaystyle 3 x+3 y=-15 </code></p>
<p> Multiply both sides by LCM of the denominators so that the following equation of lines does not have fraction in them.</p><p><code class='latex inline'>\displaystyle -\frac{1}{5}x + \frac{2}{21}y = -\frac{3}{7} </code></p>
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