Beginning Algebra, 11th Edition

SECTION 3.2 Graphing Linear Equations in Two Variables^191

We use the ordered pairs 1 - 6, - 22 , 1 0, 0 2 ,and 1 6, 2 2 to draw the graph in FIGURE 12.

NOW TRY
EXERCISE 3
Find the intercepts for the
graph of. Then
draw the graph.

x+ 2 y= 2

xy

04

20

44 -

y-intercept

x-intercept

2 x + y = 4

(0, 4)

(2, 0) x

y

–2 1 3 5678

1

2

3

4

6

5

(4, – 4) is used as a check.

–1–1

–2

–3

–4

FIGURE 11

x

y

(^0) (2, 0)
(0, 1)
x + 2y = 2
y-intercept
x-intercept
NOW TRY

CAUTION When choosing x- or y-values to find ordered pairs to plot, be care-

ful to choose so that the resulting points are not too close together.For example,

using and to graph may result in an inaccurate

line. It is better to choose points whose x-values differ by at least 2.

1 - 1, - 12 , 1 0, 0 2 , 1 1, 1 2 x- y= 0

OBJECTIVE 3 Graph linear equations of the form AxBy 0.

NOW TRY
EXERCISE 4
Graph. 2 x+y= 0

Graphing an Equation with x- and y-Intercepts

Graph

To find the y-intercept, let.

Let.

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

- 3 y= 0

0 - 3 y= 0 x= 0

x- 3 y= 0

x= 0

x- 3 y= 0.

EXAMPLE 4 1 0, 0 2

To find the x-intercept, let.

Let.

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

x- 0 = 0

x- 3102 = 0 y= 0

x- 3 y= 0

y= 0

The x- and y-intercepts are the samepoint,. We must select two other values

for xor yto find two other points on the graph. We choose and.

Let. Let.

y = 2 Gives Gives 1 6, 2 2 y=- 2 1 - 6, - 22

- 3 y=- 6 - 3 y= 6

6 - 3 y= 0 x= 6 - 6 - 3 y= 0 x=- 6

x- 3 y= 0 x - 3 y= 0

x= 6 x=- 6

1 0, 0 2

–6 –4 –2 0 2 4 6

–6

–4

–2

2

4

6

x

y

(0, 0)

x-intercept

and y-intercept

(6, 2)

x – 3y = 0

(– 6, –2)

FIGURE 12

xy

00

62

• 62 -

NOW TRY

x

y

0

–2

2 x + y = 0

1

4. 
   

NOW TRY ANSWERS

3. x-intercept: ;
   y-intercept: 1 0, 1 2

1 2, 0 2