Graphing Inequalities

Example: Graph the inequality

x – 3y < - 9

Step 1: Change the inequality sign (<) to an equality sign(=):

x – 3y = -9 (This graphs the line)

Step 2: Set x = 0 and solve for y:

x – 3y = -9

0 – 3y = -9 (x = 0 on the y-axis.) -3y = -9 -3 -3

y = 3 Plot the point (0,3)

-x x

-y

y

3

Plot the point (0,3)

Step 3: Set y = 0 and solve for x:

x – 3y = - 9 x –3(0) = -9 (y = 0 on the x-axis.)

x = -9 Plot the point (-9,0)

Step 4: Graph the line < > broken line -------------

y

-x

-y

x -9

3

Step 5: Which side do I shade?

Choose (0,0), as a test point, if it does not lie on the graph of the line. Substitute (0,0) for

(x, y) in the inequality.

x – 3y < - 9 0 – 3(0) < - 9 Is 0 < -9?

No.

0 is not less than -9Do not shade the side of the line that contains the point (0,0).

Shade the other side.

x

y

-x

-y

-9

3