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) 3x + 2y < 12 True or False

(1,6)

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

(1,6) 3(1) + 2(6) < 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

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

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

(3,0) 3(3) + 2(0) < 12 True

(2,2) 3(2) + 2(2) < 12 True

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

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

(3,0) 3(3) + 2(0) < 12 True

(2,2) 3(2) + 2(2) < 12 True

(4,3) 3(4) + 2(3) < 12 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 > 31) Go to where y = 32) Horizontal, Dashed3) Shade inequality

Ex. 3 Graph x < -11) Go to where x = -12) Vertical, Solid3) Shade inequality

Ex. 2 Graph y > 31) Go to where y = 32) Horizontal, Dashed3) Shade inequality

Ex. 3 Graph x < -11) Go to where x = -12) Vertical, Solid3) Shade inequality

Ex. 2 Graph y > 31) Go to where y = 32) Horizontal, Dashed3) Shade inequality

Ex. 3 Graph x < -11) Go to where x = -12) Vertical, Solid3) 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 = -4LINE: 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 = -4LINE: 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