Graphuing Linear Inequalities

y > mx + b

y ≥ mx + b

y < mx + b

y ≤ mx + b

Draw a dotted line and shade the region above the line.

Draw a solid line and shade the region above the line.

Draw a dotted line and shade the region below the line.

Draw a solid line and shade the region below the line.

Subtract 3x from both sides.

Divide both sides by -2. Remember to reverse the direction of the inequality symbol.

3x - 2y

2y

y

≤ -3x - 12

≥

The inequality has the form y ≥ mx + b, so draw a solid line.

Then, shade the region above the line.

It is a good idea to check the shading with a test point.

Substitute (0, 0) in 3x - 2y ≤ -12.

The result is 0 ≤ -12, which is false.

Since (0, 0) is not a solution, the region that contains (0, 0) should not be shaded. This agrees with the graph as we have drawn it.