5.6 – Graphing Inequalities in Two Variables Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) 3x + 2y < 12 Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) 3x + 2y < 12 True or False Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) (1,6) 3x + 2y < 12 True or False Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) 3x + 2y < 12 (1,6) 3(1) + 2(6) < 12 True or False Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) 3x + 2y < 12 (1,6) 3(1) + 2(6) < 12 True or False False Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (x, y) (1,6) (3,0) (2,2) (4,3) 3x + 2y < 12 3(1) + 2(6) < 12 3(3) + 2(0) < 12 3(2) + 2(2) < 12 3(4) + 2(3) < 12 True or False False True True False Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)}, which ordered pairs are part of the solution set for 3x + 2y < 12? (3,0) & (2,2) (x, y) (1,6) (3,0) (2,2) (4,3) 3x + 2y < 12 3(1) + 2(6) < 12 3(3) + 2(0) < 12 3(2) + 2(2) < 12 3(4) + 2(3) < 12 True or False False True True False Ex. 2 Graph y > 3 Ex. 2 Graph y > 3 Ex. 2 Graph y > 3 1) Go to where y = 3 Ex. 2 Graph y > 3 1) Go to where y = 3 Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical, Solid Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical, Solid Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical, Solid 3) Shade inequality Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical, Solid 3) Shade inequality Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1 1) Go to where x = -1 2) Vertical, Solid 3) Shade inequality Ex. 4 Graph y – 2x < -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 LINE: Solid b/c includes “equal to” Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 LINE: Solid b/c includes “equal to” Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 LINE: Solid b/c includes “equal to” SHADE: Since < shade below the line. Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4 LINE: Solid b/c includes “equal to” SHADE: Since < shade below the line. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Total number of people cannot exceed 250. Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Total number of people cannot exceed 250. So, x + y Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Total number of people cannot exceed 250. So, x + y < 250 Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Total number of people cannot exceed 250. So, x + y < 250 OR Ex. 5 Suppose a theatre can seat a maximum of 250 people. Write an inequality to represent the number of adult and childrens tickets that can be sold. Let x = # of adult tickets. Let y = # of child tickets. Total number of people cannot exceed 250. So, x + y < 250