# 4.2E: Exercises

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## Practice Makes Perfect

Recognize the Relationship Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

1. Is the ordered pair a solution to the equation?
2. Is the point on the line?

### Exercise $$\PageIndex{1}$$

y=x+2

1. (0,2)
2. (1,2)
3. (−1,1)
4. (−3,−1) 1. yes; no
2. no; no
3. yes; yes
4. yes; yes

### Exercise $$\PageIndex{2}$$

y=x−4

1. (0,−4)
2. (3,−1)
3. (2,2)
4. (1,−5) ### Exercise $$\PageIndex{3}$$

$$y=\frac{1}{2} x-3$$

1. (0,−3)
2. (2,−2)
3. (−2,−4)
4. (4,1) 1. yes; yes
2. yes; yes
3. yes; yes
4. no; no

### Exercise $$\PageIndex{4}$$

$$y=\frac{1}{3} x+2$$

1. (0,2)
2. (3,3)
3. (−3,2)
4. (−6,0) Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

### Exercise $$\PageIndex{5}$$

$$y=3 x-1$$ ### Exercise $$\PageIndex{6}$$

$$y=2 x+3$$

### Exercise $$\PageIndex{7}$$

$$y=-2 x+2$$ ### Exercise $$\PageIndex{8}$$

$$y=-3 x+1$$

### Exercise $$\PageIndex{9}$$

$$y=x+2$$ ### Exercise $$\PageIndex{10}$$

$$y=x-3$$

### Exercise $$\PageIndex{11}$$

$$y=-x-3$$ ### Exercise $$\PageIndex{12}$$

$$y=-x-2$$

### Exercise $$\PageIndex{13}$$

$$y=2 x$$ ### Exercise $$\PageIndex{14}$$

$$y=3 x$$

### Exercise $$\PageIndex{15}$$

$$y=-4 x$$ ### Exercise $$\PageIndex{16}$$

$$y=-2 x$$

### Exercise $$\PageIndex{17}$$

$$y=\frac{1}{2} x+2$$ ### Exercise $$\PageIndex{18}$$

$$y=\frac{1}{3} x-1$$

### Exercise $$\PageIndex{19}$$

$$y=\frac{4}{3} x-5$$ ### Exercise $$\PageIndex{20}$$

$$y=\frac{3}{2} x-3$$

### Exercise $$\PageIndex{21}$$

$$y=-\frac{2}{5} x+1$$ ### Exercise $$\PageIndex{22}$$

$$y=-\frac{4}{5} x-1$$

### Exercise $$\PageIndex{23}$$

$$y=-\frac{3}{2} x+2$$ ### Exercise $$\PageIndex{24}$$

$$y=-\frac{5}{3} x+4$$

### Exercise $$\PageIndex{25}$$

$$x+y=6$$ ### Exercise $$\PageIndex{26}$$

$$x+y=4$$

### Exercise $$\PageIndex{27}$$

$$x+y=-3$$ ### Exercise $$\PageIndex{28}$$

$$x+y=-2$$

### Exercise $$\PageIndex{29}$$

$$x-y=2$$ ### Exercise $$\PageIndex{30}$$

$$x-y=1$$

### Exercise $$\PageIndex{31}$$

$$x-y=-1$$ ### Exercise $$\PageIndex{32}$$

$$x-y=-3$$

### Exercise $$\PageIndex{33}$$

$$3 x+y=7$$ ### Exercise $$\PageIndex{34}$$

$$5x+y=6$$

### Exercise $$\PageIndex{35}$$

2x+y=−3 ### Exercise $$\PageIndex{36}$$

$$4x+y=−5$$

### Exercise $$\PageIndex{37}$$

$$\frac{1}{3} x+y=2$$ ### Exercise $$\PageIndex{38}$$

$$\frac{1}{2} x+y=3$$

### Exercise $$\PageIndex{39}$$

$$\frac{2}{5} x-y=4$$ ### Exercise $$\PageIndex{40}$$

$$\frac{3}{4} x-y=6$$

### Exercise $$\PageIndex{41}$$

$$2 x+3 y=12$$ 4x+2y=12

### Exercise $$\PageIndex{43}$$

3x−4y=12 2x−5y=10

### Exercise $$\PageIndex{45}$$

x−6y=3 x−4y=2

### Exercise $$\PageIndex{47}$$

5x+2y=4 ### Exercise $$\PageIndex{48}$$

3x+5y=5

Graph Vertical and Horizontal Lines

In the following exercises, graph each equation.

### Exercise $$\PageIndex{49}$$

x=4 x=3

### Exercise $$\PageIndex{51}$$

x=−2 x=−5

### Exercise $$\PageIndex{53}$$

y=3 y=1

### Exercise $$\PageIndex{55}$$

y=−5 y=−2

### Exercise $$\PageIndex{57}$$

$$x=\frac{7}{3}$$ ### Exercise $$\PageIndex{58}$$

$$x=\frac{5}{4}$$

### Exercise $$\PageIndex{59}$$

$$y=-\frac{15}{4}$$ ### Exercise $$\PageIndex{60}$$

$$y=-\frac{5}{3}$$

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

### Exercise $$\PageIndex{61}$$

y=2x and y=2 y=5x and y=5

### Exercise $$\PageIndex{63}$$

$$y=-\frac{1}{2} x$$ and $$y=-\frac{1}{2}$$ ### Exercise $$\PageIndex{64}$$

$$y=-\frac{1}{3} x$$ and $$y=-\frac{1}{3}$$

## Mixed Practice

In the following exercises, graph each equation.

### Exercise $$\PageIndex{65}$$

y=4x y=2x

### Exercise $$\PageIndex{67}$$

$$y=-\frac{1}{2} x+3$$ ### Exercise $$\PageIndex{68}$$

$$y=\frac{1}{4} x-2$$

### Exercise $$\PageIndex{69}$$

y=−x y=x

### Exercise $$\PageIndex{71}$$

x−y=3 x+y=−5

### Exercise $$\PageIndex{73}$$

4x+y=2 2x+y=6

### Exercise $$\PageIndex{75}$$

y=−1 y=5

### Exercise $$\PageIndex{77}$$

2x+6y=12 5x+2y=10

### Exercise $$\PageIndex{79}$$

x=3 x=−4

## Everyday Math

### Exercise $$\PageIndex{81}$$

Motor home cost. The Robinsons rented a motor home for one week to go on vacation. It cost them $594 plus$0.32 per mile to rent the motor home, so the linear equation y=594+0.32x gives the cost, yy, for driving xx miles. Calculate the rental cost for driving 400, 800, and 1200 miles, and then graph the line.

## Writing Exercises

### Exercise $$\PageIndex{83}$$

Explain how you would choose three $$x$$ - values to make a table to graph the line $$y=\frac{1}{5} x-2$$

### Exercise $$\PageIndex{84}$$

What is the difference between the equations of a vertical and a horizontal line?

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ After reviewing this checklist, what will you do to become confident for all goals?

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