Beginning Algebra, 11th Edition

SECTION 3.5 Graphing Linear Inequalities in Two Variables^223

19.Concept Check Match the description in Column I with the correct equation in

Column II.

III

(a) A.

(b)x-intercept , y-intercept B.

(c) Passes through and C.

(d) , passes through D.

E.

20.Concept Check Which equations are equivalent to

A. B.

C. D.

Write an equation for each line. Give the final answer in slope-intercept form if possible.

21. 
    
    
    
    22. through
        23.Through and 24.Through and
        25.Through undefined slope 26.Through and
        27.Through and 28.
        29.Through and 30.Through
        31.m= 35 ,through 1 - 3, 0 2 32.Through and 1 1, - 132 1 - 2, 2 2
    
    
    
    

1 5, 0 2 1 0, - 52 1 0, 0),m= 0

1 0, 0 2 1 3, 2 2 m=-2, b=- 4

1 0, 0), 1 3, 0 2 1 0, - 32

1 1, - 72 1 - 2, 5 2 1 0, 0 2 1 5, 3 2

m=-3, b=- 6 m=^32 , 1 - 4, 6 2

y= 2 x= 5 y- 20

5

2

x- 4

y- 2 =-

2

5

y=- (x- 52

2

5

x+ 4

2 x+ 5 y=20?

x= 2 y

m= 21 1 - 2, - 22 x+ 2 y= 4

1 4, - 22 1 0, 0 2 x- 2 y= 2

1 4, 0 2 1 0, 2 2 y=- 21 x- 2

Slope -0.5, b=- 2 y=- 21 x

OBJECTIVES

Graphing Linear Inequalities in Two Variables

3.5

1 Graph linear
inequalities in two
variables.

2 Graph an inequality
with a boundary
line through the
origin.

In Section 3.2,we graphed linear equations such as

We now extend this work to linear inequalities in two variables,such as

2 x+ 3 y...6.

2 x+ 3 y= 6.

Linear Inequality in Two Variables

An inequality that can be written as

,or

where A, B, and Care real numbers and Aand Bare not both 0, is a linear

inequality in two variables.

AxBy<C, AxBy◊ C AxBy>C, AxBy» C,