
# 4.3E: Exercises


## 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.

Exercise $$\PageIndex{13}$$

x+y=4

(4,0),(0,4)

Exercise $$\PageIndex{14}$$

x+y=3

Exercise $$\PageIndex{15}$$

x+y=−2

(−2,0),(0,−2)

Exercise $$\PageIndex{16}$$

x+y=−5

Exercise $$\PageIndex{17}$$

x–y=5

(5,0),(0,−5)

Exercise $$\PageIndex{18}$$

x–y=1

Exercise $$\PageIndex{19}$$

x–y=−3

(−3,0),(0,3)

Exercise $$\PageIndex{20}$$

x–y=−4

Exercise $$\PageIndex{21}$$

x+2y=8

(8,0),(0,4)

Exercise $$\PageIndex{22}$$

x+2y=10

Exercise $$\PageIndex{23}$$

3x+y=6

(2,0),(0,6)

Exercise $$\PageIndex{24}$$

3x+y=9

Exercise $$\PageIndex{25}$$

x–3y=12

(12,0),(0,−4)

Exercise $$\PageIndex{26}$$

x–2y=8

Exercise $$\PageIndex{27}$$

4x–y=8

(2,0),(0,−8)

Exercise $$\PageIndex{28}$$

5x–y=5

Exercise $$\PageIndex{29}$$

2x+5y=10

(5,0),(0,2)

Exercise $$\PageIndex{30}$$

2x+3y=6

Exercise $$\PageIndex{31}$$

3x–2y=12

(4,0),(0,−6)

Exercise $$\PageIndex{32}$$

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 $$\PageIndex{36}$$

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

Exercise $$\PageIndex{37}$$

y=3x

(0,0)

Exercise $$\PageIndex{38}$$

y=-2x

Exercise $$\PageIndex{39}$$

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 $$\PageIndex{65}$$

$$y=x$$

Exercise $$\PageIndex{66}$$

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 $$\PageIndex{72}$$