1. Linear Inequalities in Two Variables
6.8
Linear Inequalities in Two Variables

2. To Graph Inequalities in Two Variables
Mentally substitute the equal sign for the inequality sign and plot points as if you were graphing the equation.
If the inequality is < or >, draw a dashed line through the points. If the inequality is  or , draw a solid line through the points.
Select a test point not on the line and substitute the x and y-coordinates into the inequality. If the substitution results in a true statement, shade the area on the same side of the line as the test point. If the test point results in a false statement, shade the area on the opposite side of the line as the test point.

3. Example: Graph 3x + 4y > 12
Think: 3x + 4y = 12
Draw a dashed line.
Select a test point.
Try (0, 0)
3x + 4y > 12
3(0) + 4(0) > 12
0 + 0 > 12
0 > 12 false
Shade the opposite half plane.

4. Graph y > -3x - 2

5. Example: Graph 3x + y  6 Think: 3x + y = –6 Draw a solid line.
Select a test point.
Try (0, 0)
3x + y  6
3(0) + (0)  6
0 + 0  6
0  6 false
Shade the opposite half plane.

6. Graph x – 2y > 4

7. Example: Graph y > 2 Think: y = –2 Draw a dashed line.
Select a test point.
Try (0, 0)
0 > 2 true
Shade the half plane containing (0, 0).

8. Graph x > 2 on a coordinate plane

9. Homework
P. 351 #
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