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2.6 Graphing linear Inequalities in 2 Variables

- p. 108

Checking Solutions

- An ordered pair (x,y) is a solution if it makes

the inequality true. - Are the following solutions to
- 3x 2y 2
- (0,0) (2,-1) (0,2)

3(0) 2(2) 2 4 2 Is a solution

3(2) 2(-1) 2 4 2 Is a solution

3(0) 2(0) 2 0 2 Not a solution

To sketch the graph of a linear inequality

- Sketch the line given by the corresponding

equation (solid if or , dashed if lt or gt).

This line separates the coordinate plane into 2

half-planes. In one half-plane all of

the points are solutions of the inequality.

In the other half-plane - no point is a

solution - You can decide whether the points in an entire

half-plane satisfy the inequality by testing ONE

point in the half-plane. - Shade the half-plane that has the solutions to

the inequality.

The graph of an inequality is the graph of all

the solutions of the inequality

- 3x 2y 2
- y -3/2x 1 (put into slope intercept to

graph easier) - Graph the line that is the boundary of 2 half

planes - Before you connect the dots check to see if the

line should be solid or dashed - solid if or
- dashed if lt or gt

y -3/2x 1

Step 1 graph the boundary

(the line is solid )

Step 2 test a point NOT On the line (0,0) is

always The easiest if its Not on the line!!

3(0) 2(0) 2 0 2 Not a solution

So shade the other side of the line!!

Graph y lt 6

4x 2y lt 7

Assignment

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