Graphing a Linear Inequality

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 lt or gt, the line
• is dotted. If the inequality is or
• , the line is solid.

3
Graphing a Linear Inequality

• Graph the inequality 3 - x gt 0
• First, solve the inequality for x.
• 3 - x gt 0
• -x gt -3
• x lt 3

4
Graph xlt3

• Graph the line x 3.
• Because x lt 3 and
• not x 3, the line
• will be dotted.
• Now shade the side
• of the line where
• x lt 3 (to the left of
• the line).

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 gt 0
• 3 1 gt 0
• 2 gt 0
• True! The inequality
• has been graphed
• correctly.