Graphing Linear Inequalities

Graphing Linear Inequalities

If you can graph a straight line, you can graph an inequality!

Graphing an inequality starts by graphing the corresponding straight line. After graphing the line, there are only two additional steps to remember.

1. Choose a point not on the line and see if it makes the inequality true. If the inequality is true, you will shade THAT side of the line — thus shading OVER the point. If it is false, you will shade the OTHER side of the line — not shading OVER the point.
2. If the inequality is LESS THAN OR EQUAL TO or GREATER THAN OR EQUAL TO, the line is drawn as a solid line. If the inequality is simply LESS THAN or GREATER THAN, the line is drawn as a dashed line.

Graphing an Inequality

1. Solve the equation for y (if necessary).
2. Graph the equation as if it contained an = sign.
3. Draw the line solid if the inequality is ≤ or ≥.
4. Draw the line dashed if the inequality is < or >.
5. Pick a point not on the line to use as a test point.
6. The point (0,0) is a good test point if it is not on the line.
7. If the point makes the inequality true, shade that side of the line. If the point does not make the inequality true, shade the opposite side of the line.

Example: Graph the following inequality y ≤ 3x – 1.