1. Graphing Linear Inequalities
Section 3.5
Graphing Linear Inequalities

2. Inequalities
An inequality is a statement that describes how two numbers are related to one another. 2
– 2 1 3 4 5
– 1
– 3
– 4
– 5
– 4 < – 1
– 1 > – 4
“is less than”
“is greater than”
– 4  – 1
– 1  – 4
“is less than or equal to”
“is greater than or equal to”

3. Graphing Linear Inequalities
Replace the inequality symbol by an equality symbol. Graph the line.
The line will be solid if the inequality is  or .
The line will be dashed if the inequality is > or <.
Test the point (0, 0) in the inequality if (0, 0) does not lie on the graphed line in step 1.
If the inequality is true, shade the region on the side of the line that includes (0, 0).
If the inequality is false, shade the region on the side of the line that does not include (0, 0).
If the point (0, 0) is a point on the line, choose another test point and proceed accordingly.

4. Example Graph 2x + 5y  10. Graph the line 2x + 5y = 10.
Look for a test point. y x 1 4
The solid line indicates that the line is part of the solution.
Is (0, 0) a solution?
2x + 5y  10
2(0) + 5(0)  10
0  9
False
(0, 0) is not included in the solution.

5. Example Graph y < – 3x + 9 Graph the line y = – 3x + 9.4
The dashed line indicates that the line is not part of the solution.
Look for a test point.
Is (0, 0) a solution?
y < – 3x + 9
0 < – 3(0) + 9
0 < 9
True
(0, 0) is included in the solution.

6. Example
Graph x > 2. Graph x = 2 The line will be dashed. Test (0, 0) in the inequality. x > 2 0 > 2 false Shade the region that does not include (0, 0).