Chapter 7 Section 5

Graphing Linear Inequalities

Learning Objective

Graph a linear inequalities in two variables.

Key Vocabulary: linear inequalities in two variablescoordinate plane region

Graphing Linear Inequalities

Linear inequalities is when you replace the equal sign with an inequality sign. > < ≤ ≥

There are two regions: one above the equation line one below the equation line

2

1

y

x

Equation

Graphing Linear Inequalities

Examples: For each inequality, determine if the boundary line for the graph will be dashed or solid.

a) 3x < 4y dashed line

b) 2x + 3y ≥ 72 solid line

c) -3x – 4y ≤ 13 solid line

d) -5x + 11y > 41 dashed line

Graphing Linear Inequalities

EXAMPLES: Determine if the ordered pair (3, -2) is a solution to the inequality

a) 4x – 3y > 3 b) -2x + 5y ≤ 04(3) – 3(-2) > 3 -2(3) + 5(-2) ≤ 012 + 6 > 3 -6 – 10 ≤ 018 > 3 -16 ≤ 0True True

c) 4x + 7y ≥ 2 d) 8x + 3y < -54(3) + 7(-2) ≥ 2 8(3) + 3(-2) < -512 – 14 ≥ 2 e) 3x + 9y ≤ -9 24 – 6 < -5-2 ≥ 2 3(3) + 9(-2) ≤ -9 18 < -5False 9 – 18 ≤ -9 False

-9 ≤ -9 True

Graphing Linear Inequalities Graph

Replace inequality with an equal sign

Solve for y and choose at least three values for x this will give you three sets of ordered pairs

Draw the graph of the equation • ≤ or ≥ draw a solid line• > or < draw a dotted line

Select any point not on the line and determine if it is a solution. A good point to choose if not on the line is (0, 0)

• If true shade that region• If false shade the opposite region

Graphing Linear Inequalities

EXP: Graph the inequality y < x – 1 change inequality to equal sign

y = x – 1

m = 1y-intercept (0, -1) Positive slope up 1 right 1

(0,0)

(0,-1)

(2,1)

(1,0)

x y

0 -1

1 0

2 1

y < x – 1 point (0 , 0)

0 < 0 – 1

0 < -1 FALSE

Two way to graph 1.Slope Intercept2.Plotting the points

Graphing Linear InequalitiesEXP: Graph the inequality y ≥ - ⅓ xchange inequality to equal signy = - ⅓ x

m = ⅓y-intercept (0,0)

Negative slope down 1 right 3

(3,-1)

(6,-2)

x y

0 0

3 -1

6 -2

y ≥ -⅓ (x) point (3,1)1 ≥ -⅓ (3)

1 ≥ -1 TRUE

(0,0)

(3,1)

Two way to graph 1. Slope Intercept 2. Plotting the points

Graphing Linear InequalitiesEXP: Graph the inequality 3x – y > 6change inequality to equal sign

m = 3 y-intercept (0, -6)Positive slope up 3 right 1

(0,-6)

(2,0)

3 6

3 6

3 6

x y

y x

y x

x y

0 -6

1 -3

2 0

3x – y > 6 point (0,0)3(0) – 0 > 6

0 > 6 FALSE

(0,0)

(1,-3)

Two way to graph 1. Slope Intercept 2. Plotting the points

Graphing Linear Inequalities

EXP: Graph the inequality y ≤ 5change inequality to equal sign

Horizontal linem = 0

5y (2,5)

(0,0)

(-2.5)

y ≤ 5 point (0,0)

0 ≤ 5 TRUE

Graphing Linear Inequalities

EXP: Graph the inequality x > -3change inequality to equal sign

Vertical lineSlope is undefined

3x

x > -3 point (0,0)

0 > -3 True

(-3,2)

(0,0)

(-3,-2)

Remember

> and < are strict inequalities and are dashed lines on the graph

≤ and ≥ are non-strict inequalities and are solid lines on the graph

Change the inequality to and equal sign

Solve for y

Use the slope and y-intercept or use plotting points to graph the equation

Select a test point not on the line true shade that region false shade the opposite region

HOMEWORK 7.5

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