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# Graphuing Linear Inequalities

To graph a linear inequality in x and y, you may find it helpful to first solve the inequality for y. Once that has been done, the inequality can be graphed using the following guidelines:

 Inequality y > mx + b y ≥ mx + b y < mx + b y ≤ mx + b Solution 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.

Example 1

Graph the inequality 3x - 2y -12.

Solution

 First, solve the inequality for y. Subtract 3x from both sides. Divide both sides by -2. Remember to reverse the direction of the inequality symbol. 3x - 2y 2y y ≤ -12 ≤ -3x - 12 ≥ Next, graph the corresponding equation 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.