2.7 Two-Variable Inequalities

1. Graphing Linear Inequalities2. 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…– the values on the coordinate plane that

apply to the function

• What an equation looks like…

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

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)

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 >

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 >

1) Graphing Linear Inequalities

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

1) Graphing Linear Inequalities

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

Remember… y = mx + b

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

Remember… y = mx + b

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

y <

DASHED line

1) Graphing Linear Inequalities

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

m = 2

y-int = 2

y <

SHADE BELOW the line

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int =

m =

inequality type

y = mx + b

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int =

m =

inequality type

y = mx + b

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m =

inequality type

y = mx + b

1) Graphing Linear Inequalities

Example 2:Write an inequality for the graph

below.y –int = -3

m = -3/2

inequality type >

y = mx + b

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

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

Homework

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

Don’t forget…

Quiz TUESDAY

Test FRIDAY

2) Absolute Value Inequalities

• Graph the absolute value function then shade above OR below

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<

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 2:Graph –y + 1 < -2|x + 2|

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

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

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

Shade above

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

Example 3:Write an equation for the graph below.

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