Lesson 6 6 Graphing Inequalities in Two Variables

Lesson 6 -6 Graphing Inequalities in Two Variables

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 3 x + 2 y 12? . X Y 1 6 3 0 2 2 4 3 3 x + 2 y < 12 T or F o y x

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 4 x + 2 y 8? . X Y 3 3 0 2 2 4 1 0 4 x + 2 y < 8 T or F o y x

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.

Half Plane Boundary x o Half Plane y

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

Graph 2 y - 4 x > 6 Graph 2 y - 4 x 6 2 y - 4 x + 6 2 y 4 x + 6 Divide both sides by 2 y 2 x + 3 Greater than means color above the boundary. y = 2 x + 3 x o y

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. ½min ½ times the number of 30 -s commercials plus 1 -min commercials x + y is up to 15 min. 15

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 y 4 8 12 16 20 24 28 32 36 40 44

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 y 2 4 6 8 10 12 14 16 18 20 22