1. Graphing a Linear Inequality
Graphing a linear inequality is very similar to graphing a linear equation.

2. Graphing a Linear Inequality
1) Solve the inequality for y
(or for x if there is no y).
2) Change the inequality to an equation
and graph.
3) If the inequality is < or >, the line
is dotted. If the inequality is ≤ or
≥, the line is solid.

3. Graphing a Linear Inequality
Graph the inequality 3 - x > 0
First, solve the inequality for x.
3 - x > 0
-x > -3
x < 3

4. Graph: x<3 Graph the line x = 3. Because x < 3 and
not x ≤ 3, the line
will be dotted.
Now shade the side
of the line where
x < 3 (to the left of
the line). 6 4 2 3

5. Graphing a Linear Inequality
4) To check that the shading is correct, pick a
point in the area and plug it into the
inequality.
5) If the inequality statement is true, the
shading is correct. If the inequality
statement is false, the shading is incorrect.

6. Graphing a Linear Inequality
Pick a point, (1,2),
in the shaded area.
Substitute into the
original inequality
3 – x > 0
3 – 1 > 0
2 > 0
True! The inequality
has been graphed
correctly. 6 4 2 3