Beginning Algebra, 11th Edition

The intercepts are and. To find a third point, we let.

Let.

Multiply.

y=- 4 Subtract 8.

8 + y= 4

2142 + y= 4 x= 4

2 x+ y= 4

1 0, 4 2 1 2, 0 2 x= 4

190 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

x

y

(–2, 6) is used as a check.

(0, 3)

(2, 0)

y = x + 3

–2–1 1234

6 5 4 3 2 1

–1

–2

3

• 2

FIGURE 10

xy

03

20

• 26

NOW TRY

OBJECTIVE 2 Find intercepts.In FIGURE 10, the graph intersects (crosses) the

y-axis at and the x-axis at For this reason, is called the y-intercept

and is called the x-interceptof the graph. The intercepts are particularly use-

ful for graphing linear equations.

1 2, 0 2

1 0, 3 2 1 2, 0 2. 1 0, 3 2

Finding Intercepts

Find the intercepts for the graph of Then draw the graph.

To find the y-intercept, let. To find the x-intercept, let

Let Let.

y = 4 y-intercept is 1 0, 4 2. x= 2 x-intercept is 1 2, 0 2.

0 +y= 4 2 x= 4

2102 +y= 4 x=0. 2 x+ 0 = 4 y= 0

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

x= 0 y= 0.

2 x+ y=4.

EXAMPLE 3

This gives the ordered pair. We plot the three ordered pairs and draw a line

through them, as shown in FIGURE 10.

1 - 2, 6 2

This gives the ordered pair The graph, with the two intercepts in red, is

shown in FIGURE 11 on the next page.

1 4, - 42.

NOW TRY

EXERCISE 2

Graph .y=^13 x+ 1

(–3, 0)^0 x

(0, 1)

y =^13 x + 1

y

NOW TRY ANSWER
2.

Finding Intercepts

To find the x-intercept, let in the given equation

and solve for x. Then is the x-intercept.

To find the y-intercept, let in the given equation

and solve for y. Then 1 0, y 2 is the y-intercept.

x= 0

1 x, 0 2

y= 0

x

y

y-intercept

x-intercept

0

(0, y)

(x, 0)

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