Textbook

9 Mathematics McGraw-Hill
Chapter

Chapter 6
Section

Chapter 4 to 6 Review(Algebra to Linear Relationship)

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Solutions
41 Videos

Solve for x.

```
\displaystyle
x-2 = -5
```

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Q1a

Solve for x.

```
\displaystyle
\frac{y}{6} = - 7
```

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Q1b

Solve for x.

```
\displaystyle
9 + w = 13
```

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Q1c

Solve for x.

```
\displaystyle
8s = 32
```

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Q1d

Solve for x.

```
\displaystyle
4n + 9 = 25
```

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Q1e

Solve for x.

```
\displaystyle
16 - 5r = -14
```

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Q1f

Solve for x.

```
\displaystyle
5x - 8 = 2x + 7
```

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Q2a

Solve for x.

```
\displaystyle
-2y - 7 = 4y + 11
```

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Q2b

Solve for x.

```
\displaystyle
4(3w + 2) = w - 14
```

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Q2c

Solve for x.

```
\displaystyle
3 - 2(s -1) = 13 + 6s
```

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Q2d

Solve for x.

```
\displaystyle
2(n + 9) = -6(2n -5) + 8
```

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Q2e

Solve for x.

```
\displaystyle
5(4k -3) - 5k = 10 + 2(3k + 1)
```

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Q2f

Solve for x.

An isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.

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Q3

Solve for x.

```
\displaystyle
\frac{x + 6}{5} = -2
```

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Q4a

Solve for x.

```
\displaystyle
6 = \frac{2}{5} (n -1)
```

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Q4b

Solve for x.

```
\displaystyle
\frac{y +3}{2} = \frac{y - 4}{3}
```

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Q4c

Solve for x.

```
\displaystyle
\frac{1}{4}(k -3) = \frac{1}{5}(k + 1)
```

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Q4d

Rearrange each formula to isolate the variable indicated.

`A = P + I`

, for `P`

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Q5a

Rearrange each formula to isolate the variable indicated.

`d =2r`

, for `r`

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Q5b

Rearrange each formula to isolate the variable indicated.

`v =u + at`

, for `a`

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Q5c

Rearrange each formula to isolate the variable indicated.

`P = 2(l + w)`

, for `l`

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Q5d

International basketball competitions are played on a rectangular court where the length is 2m less than twice the width.

a) If the perimeter of the court is 867m, what are the dimensions of the courts?

b) Solve this problem using a different method.

c) Compare the methods. Describe one advantage and one disadvantage of each approach.

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Q6

Natalie's pay varies directly with the time she works. She earns `\displaystyle \$ 45 `

for `\displaystyle 5 \mathrm{~h} `

.

a) Describe the relationship in words.

b) Write an equation relating her pay and the time worked. What does the constant of variation represent?

c) How much will Natalie earn for `\displaystyle 9 \mathrm{~h} `

worked?

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Q7

The table shows the cost, `C`

, in dollars, to rent a car for a day and drive a distance, `d`

, in kiliometres.

```
\displaystyle
\begin{array}{|c|c|}
\hline Distance, \boldsymbol{d}(\mathbf{k m}) & Cost, C (\$) \\
\hline 0 & 50 \\
\hline 100 & 65 \\
\hline 200 & 80 \\
\hline 300 & 95 \\
\hline 400 & 110 \\
\hline
\end{array}
```

a) What is the fixed cost?

b) What is the variable cost? Explain how you found this.

c) Write an equation relating to C and d.

d) What is the cost of renting a car for a day and driving 750 km?

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Q8

Find the slope of each line segment.

a) `\displaystyle \mathrm{AB} `

c) `\displaystyle \mathrm{EF} `

b) `\displaystyle \mathrm{CD} `

d) `\displaystyle \mathrm{GH} `

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Q9

A racehorse can run `\displaystyle 6 \mathrm{~km} `

in `\displaystyle 5 \mathrm{~min} `

.

a) Calculate the rate of change of the horse's distance.

b) Graph the horse's distance as it relates to time.

c) Explain the meaning of the rate of change and how it relates to the graph.

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Q10

Classify each relation as linear or non-linear.

```
\displaystyle
\begin{array}{|c|c|}
\hline x & y \\
\hline 0 & 5 \\
\hline 1 & 7 \\
\hline 2 & 9 \\
\hline 3 & 11 \\
\hline 4 & 13 \\
\hline
\end{array}
```

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Q11a

Classify each relation as linear or non-linear.

```
\displaystyle
\begin{array}{|c|c|}
\hline x & y \\
\hline 0 & -4 \\
\hline 2 & -2 \\
\hline 4 & 2 \\
\hline 6 & 8 \\
\hline 8 & 16 \\
\hline
\end{array}
```

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Q11b

Use the rule of four to represent this other ways.

a) Use a graph.

b) Use words.

c) Use an equation.```
\displaystyle
\begin{array}{|r|r|}
\hline x & y \\
\hline 0 & 4 \\
\hline 5 & 8 \\
\hline 10 & 12 \\
\hline 15 & 16 \\
\hline 20 & 20 \\
\hline
\end{array}
```

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Q12

For the line,

- identify the slope and the y-intercept.
- write the equation of the line in slope y-intercept form.

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Q13a

For the line,

- identify the slope and the y-intercept.
- write the equation of the line in slope y-intercept form.

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Q13b

a) Rearrange `\displaystyle 3 x-4 y+8=0 `

into the form `\displaystyle y=m x+b `

b) Identify the slope and the `\displaystyle y `

-intercept.

c) Use this information to graph the line.

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Q14

Determine the `x`

and `y`

-intercepts.

```
\displaystyle
3x - y = 6
```

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Q15a

Determine the `x`

and `y`

-intercepts.

```
\displaystyle
-2x + 5y = 15
```

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Q15b

Classify each pair of lines as parallel, perpendicular, or neither. Explain.

`y = 2x + 5`

```
\displaystyle
y = - \frac{1}{2}x -2
```

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Q16a

Classify each pair of lines as parallel, perpendicular, or neither. Explain.

`y = -3x + 2`

```
\displaystyle
y = -3x -8
```

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Q16b

Classify each pair of lines as parallel, perpendicular, or neither. Explain.

`y = \frac{3}{4}x + 2`

```
\displaystyle
y = \frac{4}{3}x -2
```

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Q16c

Classify each pair of lines as parallel, perpendicular, or neither. Explain.

`y =3, x = -2`

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Q16d

Find the equation of the line which passes through the following points:

```
\displaystyle
(3, 2)
```

and ```
\displaystyle
(6, 3)
```

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Q17a

Find the equation of the line which passes through the following points:

```
\displaystyle
(-2, 3)
```

and ```
\displaystyle
(1, -3)
```

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Q17b

An online music download site offers two monthly plans:

- Plan A: $10 plus $1 per download
- Plan B: $1.50 per download

a) Graph this linear system and find the solution.

b) Explain the conditions under which each plan is better.

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Q18