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2.7 Two-Variable Inequalities 1. Graphing Linear Inequalities 2. Graphing Absolute-Value Inequalities

2.7 Two-Variable Inequalities

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2.7 Two-Variable Inequalities. Graphing Linear Inequalities Graphing Absolute-Value Inequalities. 1) Graphing Linear Inequalities. The graph of a linear inequality is a region of the coordinate plane that is bounded by a line. 1) Graphing Linear Inequalities. What it shows… - PowerPoint PPT Presentation

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Page 1: 2.7 Two-Variable Inequalities

2.7 Two-Variable Inequalities

1. Graphing Linear Inequalities2. Graphing Absolute-Value

Inequalities

Page 2: 2.7 Two-Variable Inequalities
Page 3: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

• The graph of a linear inequality is a region of the coordinate plane that is bounded by a line

Page 4: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

• What it shows…– the values on the coordinate plane that

apply to the function

• What an equation looks like…

Page 5: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

• What it shows…– the values on the coordinate plane that

apply to the function

• What an equation looks like…1) Inequality

symbol

2) Slope

3) y-intercept

Page 6: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

• What linear inequality graphs look like…1) boundary line

(solid or dashed)

2) shaded area (above or below the boundary

line)

Page 7: 2.7 Two-Variable Inequalities

1) Graphing Linear InequalitiesA dashed boundary line

means the line is NOT part of the solution

The shading is ABOVE the boundary line if the equation is of the form

y > OR y >

y < OR y >

Page 8: 2.7 Two-Variable Inequalities

1) Graphing Linear InequalitiesA solid boundary line

means the line IS part of the solution

The shading is BELOW the boundary line if the equation is of the form

y < OR y <

y < OR y >

Page 9: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

Page 10: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

Remember… y = mx + b

Page 11: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

Remember… y = mx + b

Page 12: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

Page 13: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

Page 14: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

Page 15: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

y <

DASHED line

Page 16: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 1:Graph the inequality y < 2x + 2

m = 2

y-int = 2

y <

SHADE BELOW the line

Page 17: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.

Page 18: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int =

m =

inequality type

y = mx + b

Page 19: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int =

m =

inequality type

y = mx + b

Page 20: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m =

inequality type

y = mx + b

Page 21: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m = -3/2

inequality type >

y = mx + b

Page 22: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m = -3/2

inequality type >

Sub into y > mx + b

Page 23: 2.7 Two-Variable Inequalities

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m = -3/2

inequality type >

Sub into y > mx + b y > -3x/2- 3

Page 24: 2.7 Two-Variable Inequalities

Homework

• p.104 #1, 5, 7, 20, 21, 23, 26, 37, 38

Don’t forget…

Quiz TUESDAY

Test FRIDAY

Page 25: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

• Graph the absolute value function then shade above OR below

Page 26: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

• Graph the absolute value function then shade above OR below

Solid line…y <, y>

Dashed line…y<, y>Shade above y>, y>

Shade below…y<, y<

Page 27: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

Page 28: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 29: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 30: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 31: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 32: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 33: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

Page 34: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 2:Graph –y + 1 < -2|x + 2|

Page 35: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 2:Graph –y + 1 < -2|x + 2|

-y < -2|x + 2| - 1

y > 2|x + 2| + 1-y so CHANGE the direction of the inequality

Page 36: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Page 37: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Vertex = (-2, 1)Slope = 2Solid line

Shade above

Page 38: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Page 39: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Page 40: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Page 41: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Page 42: 2.7 Two-Variable Inequalities

2) Absolute Value Inequalities

Example 3:Write an equation for the graph below.

Page 43: 2.7 Two-Variable Inequalities

Homework

p.104 #11-13, 22, 30, 39-42

Reminders…Quiz TUESDAY (2.5, 2.6, first half 2.7)Review WEDNESDAY, THURSDAYTest FRIDAY (Chapter 2 ONLY)

Extra-help WEDNESDAY at LUNCH