1. Graphing Inequalities in Two Variables
Lesson 6-6
Graphing Inequalities in Two Variables

2. Ordered Pairs that Satisfy an Inequality
Ex 1
Ordered Pairs that Satisfy an Inequality
From 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 2 4

3. Ordered Pairs that Satisfy an Inequality
From the set {(3, 3), (0, 2), (2, 4), (1, 0)}, which ordered pairs are part of the solution set for 4x + 2y  8?. X Y
4x + 2y < 8
T or F 3 2 4 1 x o y

4. 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.

5. o x y
Half Plane
Boundary
Half Plane

6. Graph an Inequality Ex. 2 Graph y - 2x  - 4 y - 2x + 2x  2x - 4
Less than means color
below the boundary. o x y
y = 2x - 4

7. Graph 2y - 4x > 6
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. o x y
y = 2x + 3

8. Write and Solve an Inequality
Ex. 3
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?
Let x = number of 30-second commercials, and y = number of 60-second commercials.
the number of
30-s commercials
the number of
1-min commercials is
up to
½min
times
15 min.
plus  x + y  15

9. Write and Solve an Inequality
Ex. 3
½x + y  15 20 18 16
½x + y = 15 14 12 10 8 6 4 2 x o 4 8 12 16 20 24 28 32 36 40 44 y

10. Write and Solve an Inequality
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?
½x + y  8 20 18 16
½x + y = 8 14 12 10 8 6 4 2 o 2 4 6 8 10 12 14 16 18 20 22 y