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5.6 – Graphing Inequalities in Two Variables

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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?

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(x, y)

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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

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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 < 12True or False

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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 < 12True or False (1,6)

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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 < 12True or False (1,6)(1,6)3(1) + 2(6) < 12

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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 < 12True or False (1,6)3(1) + 2(6) < 12False

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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 < 12True or False (1,6)3(1) + 2(6) < 12False (3,0)3(3) + 2(0) < 12True (2,2)3(2) + 2(2) < 12True (4,3)3(4) + 2(3) < 12False

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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)3x + 2y < 12True or False (1,6)3(1) + 2(6) < 12False (3,0)3(3) + 2(0) < 12True (2,2)3(2) + 2(2) < 12True (4,3)3(4) + 2(3) < 12False

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Ex. 2 Graph y > 3

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1) Go to where y = 3

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Ex. 2 Graph y > 3 1) Go to where y = 3

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality

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Ex. 2 Graph y > 3 1) Go to where y = 3 2) Horizontal, Dashed 3) Shade inequality Ex. 3 Graph x < -1

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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

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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

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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

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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

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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

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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

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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

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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

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Ex. 4 Graph y – 2x < -4

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y – 2x < -4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4

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Ex. 4 Graph y – 2x < -4 y – 2x < -4 +2x +2x y < 2x – 4 GRAPH: y = 2x – 4 m = 2, b = -4

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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”

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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”

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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.

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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.

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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.

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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.

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Let y = # of child tickets.

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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.

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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.

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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

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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

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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

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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

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