Beginning Algebra, 11th Edition

Graphing a Linear Inequality with a Vertical Boundary Line

Graph

First, we graph a vertical line passing through the point We use a

dashed line (why?) and choose as a test point.

Original inequality

Let

True

Since is true, we shade the region containing as in FIGURE 38.

NOW TRY

OBJECTIVE 2 Graph an inequality with a boundary line through the

origin. If the graph of an inequality has a boundary line that goes through the ori-

gin, cannot be used as a test point.

Graphing a Linear Inequality with a Boundary Line

through the Origin

Graph

Graph using a solid line. Some ordered pairs that can be used to graph

this line are and Since is onthe line it cannot be

used as a test point. Instead, we choose a test point offthe line, say

Original inequality

Let and

1 ... 6 True

1 ... x= 1 y=3.

?

2132

x... 2 y

1 1, 3 2.

1 0, 0 2 , 1 6, 3 2 , 1 4, 2 2. 1 0, 0 2 x= 2 y,

x= 2 y,

x... 2 y.

EXAMPLE 4

1 0, 0 2

063 1 0, 0 2 ,

0 63

06 x=0.

?

3

x 6 3

1 0, 0 2

x=3, 1 3, 0 2.

x 6 3.

EXAMPLE 3

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

NOW TRY
EXERCISE 3
Graph .x 72

x

y

0

3

x < 3 x = 3

(0, 0)

FIGURE 38

NOW TRY ANSWER
3.

x

y

(^02)
x > 2
Be careful to draw
a dashed line.
Graphing a Linear Inequality
Step 1 Graph the boundary.Graph the line that is the boundary of the
region. Use the methods of Section 3.2.Draw a solid line if the in-
equality has or because of the equality portion of the symbol.
Draw a dashed line if the inequality has or
Step 2 Shade the appropriate region.Use any point not on the line as a
test point. Substitute for xand yin the inequality.If a true statement
results, shade the region containing the test point. If a false state-
ment results, shade the other region.

6 7.

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