Lesson 6-6

Graphing Inequalities in Two Variables

Ex 1 Ordered Pairs that Satisfy an InequalityFrom the set {(1, 6), (3, 0), (2, 2), (4, 3)}, which ordered pairs are part of the solution set for 3x + 2y 12?.

o x

y

X Y 3x + 2y < 12 T or F

1 6

3 0

2 2

4 3

Ordered Pairs that Satisfy an InequalityFrom the set {(3, 3), (0, 2), (2, 4), (1, 0)}, which ordered pairs are part of the solution set for 4x + 2y 8?.

o x

y

X Y 4x + 2y < 8 T or F

3 3

0 2

2 4

1 0

Definitions• Half Planes- Any line in the plane

divides the plane into two regions called half planes.

• Boundary- The line that divides the plane into two half planes is the boundary.

ox

y

Half Plane

Half Plane

Boundary

ox

y

Graph y - 2x - 4

y - 2x + 2x 2x - 4

y 2x - 4

Less than means color

below the boundary.

y = 2x - 4

Ex. 2 Graph an Inequality

ox

y

Graph 2y - 4x 6

2y - 4x + 4x 4x + 6

2y 4x + 6

Divide both sides by 2

y 2x + 3

Greater than means color

above the boundary.

y = 2x + 3

Graph 2y - 4x > 6

Rosa Padilla sells radio advertising in 30-second and 60-second time slots. During every hour, there are up to 15 minutes available for commercials. How many commercial slots can she sell for one hour of broadcasting?

Ex. 3 Write and Solve an Inequality

Let x = number of 30-second commercials, and y = number of 60-second commercials.

½min times the number of30-s commercials plus

the number of 1-min commercials

is up to

15 min.

½ x + y 15

Ex. 3 Write and Solve an Inequality

½x + y 15

o x

y

2

4

6

8

10

12

14

16

18

20

4 8 12 16 20 24 28 32 36 40 44

½x + y = 15

Lee Cooper writes and edits short articles for a local newspaper. It generally takes her an hour to write an article and about a half-hour to edit an article. If Lee works up to 8 hours a day, how many articles can she write and edit in one day?

Write and Solve an Inequality

½x + y 8

o

y

2

4

6

8

10

12

14

16

18

20

2 4 6 8 10 12 14 16 18 20 22

½x + y = 8