Advanced Algebra NotesSection 2.8: Graphing Linear Inequalities in Two Variables

The solution to a linear inequality in two variables is an ordered pair that makes the inequality _______. Example 1: Tell whether the following ordered pairs are solutions to the inequality 2x – 3y > -2.

A) (0, 0) B) (0, 1) C) (2, -1)

The graph of a linear inequality in two variables is a ________ or _________ half plane. Open half-plane means the boundary is not included, so we graph a ____________.

( < or > ) Closed half-plane means the boundary is included, so we graph a ___________.

( < or > )

2(0) – 3(0) > -2 0 > -2

Yes, solution

true

2(0) – 3(1) > -2 -3 > -2

No, not a solution

2(2) – 3(-1) > -2 4 + 3 > -2 7 > -2

Yes, a solutionopen closed

dotted line

solid line

Steps to Graphing a Linear Inequality in Two Variables 1.

2.

3.

4.

5.

Graph 2 points on the coordinate plane using y = mx + b or x & y intercept method.

Draw a dotted or solid line through the 2 points depending on the symbol in the problem.

Pick a test point that is not on the line you drew in step 2.

Plug the test point into the original inequality to see if it gives you a true or falsestatement.

If true, shade the side of the graph with the test point and if false, shade the other side of the graph not containing the test point.

Examples:

2) x > -2 3) y < 1

2 0

2 2

x y

Test Pt. (0, 0) 0 > -2

True

0 1

2 1

x yTest Pt. (0, 0)

0 < 1

True

4) x + y > 3 5) y > 2x – 3

0 3

3 0

x y Test Pt. (0, 0)

0 + 0 > 3 0 > 3

False

2

13 (0, 3)

m

b

Test Pt. (0, 0)

0 > 2(0) – 3 0 > -3

True

6) 7)xy3

2

2 2

3 30 (0,0)

m

b

Can’t use (0, 0) as a test pt.

Test Pt. (0, 3)

3 < -2/3(0) 3 < 0

False

a = -1 , down , base shape

V (-2, -1)Test Pt. (0, 0)

0 > -|0 + 2| - 1 0 > - 2 – 1 0 > -3

True

Page 135: 8-18 Even, 31-37 Odd