# 4.3E: Exercises

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## Practice Makes Perfect

Identify the x- and y- Intercepts on a Graph

In the following exercises, find the x- and y- intercepts on each graph.

##### Exercise $$\PageIndex{1}$$ (3,0),(0,3)

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

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

##### Exercise $$\PageIndex{6}$$ ##### Exercise $$\PageIndex{7}$$ (−1,0),(0,1)

##### Exercise $$\PageIndex{8}$$ ##### Exercise $$\PageIndex{9}$$ (6,0),(0,3)

##### Exercise $$\PageIndex{10}$$ ##### Exercise $$\PageIndex{11}$$ (0,0)

##### Exercise $$\PageIndex{12}$$ Find the x- and y- Intercepts from an Equation of a Line

In the following exercises, find the intercepts for each equation.

x+y=4

(4,0),(0,4)

x+y=3

x+y=−2

(−2,0),(0,−2)

x+y=−5

x–y=5

(5,0),(0,−5)

x–y=1

x–y=−3

(−3,0),(0,3)

x–y=−4

x+2y=8

(8,0),(0,4)

x+2y=10

3x+y=6

(2,0),(0,6)

3x+y=9

x–3y=12

(12,0),(0,−4)

x–2y=8

4x–y=8

(2,0),(0,−8)

5x–y=5

2x+5y=10

(5,0),(0,2)

2x+3y=6

3x–2y=12

(4,0),(0,−6)

3x–5y=30

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

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

(-3,0),(0,1)

##### Exercise $$\PageIndex{34}$$

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

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

$$y=\frac{1}{5} x+2$$

(−10,0),(0,2)

##### Exercise $$\PageIndex{36}$$

$$y=\frac{1}{3} x+4$$

y=3x

(0,0)

y=-2x

y=-4x

(0,0)

##### Exercise $$\PageIndex{40}$$

y=5x

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

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

$$-x+5 y=10$$ ##### Exercise $$\PageIndex{42}$$

$$-x+4 y=8$$

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

$$x+2 y=4$$ ##### Exercise $$\PageIndex{44}$$

$$x+2 y=6$$

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

$$x+y=2$$ ##### Exercise $$\PageIndex{46}$$

$$x+y=5$$

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

$$x+y=-3$$ ##### Exercise $$\PageIndex{48}$$

$$x+y=-1$$

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

$$x-y=1$$ ##### Exercise $$\PageIndex{50}$$

$$x-y=2$$

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

$$x-y=-4$$ ##### Exercise $$\PageIndex{52}$$

$$x-y=-3$$

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

$$4 x+y=4$$ ##### Exercise $$\PageIndex{54}$$

$$3 x+y=3$$

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

$$2 x+4 y=12$$ ##### Exercise $$\PageIndex{56}$$

$$3 x+2 y=12$$

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

$$3 x-2 y=6$$ ##### Exercise $$\PageIndex{58}$$

$$5 x-2 y=10$$

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

$$2 x-5 y=-20$$ ##### Exercise $$\PageIndex{60}$$

$$3 x-4 y=-12$$

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

$$3 x-y=-6$$ ##### Exercise $$\PageIndex{62}$$

$$2 x-y=-8$$

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

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

$$y=-4 x$$

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

$$y=x$$ y=3x

## Everyday Math

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

Road trip. Damien is driving from Chicago to Denver, a distance of 1000 miles. The x- axis on the graph below shows the time in hours since Damien left Chicago. The y- axis represents the distance he has left to drive. 1. Find the x- and y- intercepts.
2. Explain what the x- and y- intercepts mean for Damien.
1. (0,1000),(15,0)
2. At (0,1000), he has been gone 0 hours and has 1000 miles left. At (15,0), he has been gone 15 hours and has 0 miles left to go.
##### Exercise $$\PageIndex{68}$$

Road trip. Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank. 1. Find the x- and y- intercepts.
2. Explain what the x- and y- intercepts mean for Ozzie.

## Writing Exercises

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

How do you find the $$x$$ -intercept of the graph of $$3 x-2 y=6 ?$$

##### Exercise $$\PageIndex{70}$$

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation 4x+y=−4? Why?

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

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $$y=\frac{2}{3}x−2$$? Why?

##### Exercise $$\PageIndex{72}$$

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation y=6? Why?

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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