Intermediate Algebra (11th edition)

CAUTION A common error in using the method just described is to use the

original inequality symbol when deciding which half-plane to shade. Be sure to use

the inequality symbol found in the inequality afterit is solved for y.

Graphing a Linear Inequality

Graph

Step 1 First graph the boundary line 3 x+ 2 y= 6,as shown in FIGURE 37.

3 x+ 2 yÚ6.

EXAMPLE 1

176 CHAPTER 3 Graphs, Linear Equations, and Functions

NOW TRY
EXERCISE 1
Graph .-x+ 2 yÚ 4

2

3

0

x

y

3x + 2y = 6

FIGURE 37

Step 2 The graph of the inequality includes the points of the line

and either the points abovethat line or the points belowit. To

decide which, select any point not on the boundary line to use as a test point.

Substitute the values from the test point, here , for xand yin the inequality.

Original inequality

Let and.

False

Step 3 Because the result is false, does notsatisfy the inequality. The solution

set includes all points on the other side of the line. See FIGURE 38.

1 0, 0 2

0 Ú 6

3102 + 2102 Ú x= 0 y= 0

?

6

3 x+ 2 yÚ 6

1 0, 0 2

3 x+ 2 y= 6

3 x+ 2 yÚ 6

FIGURE 38 NOW TRY

If the inequality is written in the form or then the

inequality symbol indicates which half-plane to shade.

If then shade abovethe boundary line.

If then shade belowthe boundary line.

This method works only if the inequality is solved for y.

y 6 mx+b,

y 7 mx+ b,

y 7 mx+b y 6 mx+b,

NOW TRY ANSWER

1. 
   

2

0

y

–4 x

• x + 2y ê 4

is a

convenient

test point.

1 0, 0 2

2

3

0

3x + 2y = 6

xx

y

(0, 0)

3x + 2y^6