1. Graphing Inequalities

2. Example: Graph the inequality
x – 3y < - 9
Step 1: Change the inequality sign (<) to an
equality sign(=):
x – 3y = -9 (This graphs the line)

3. 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)

4. -x x
-y
y
3
Plot the point (0,3)

5. 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)

6. Step 4: Graph the line
< > broken line -------------
y
-x
-y
x
-9
3

7. 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.

8. 0 is not less than -9
Do not shade the side of the line that contains the point (0,0).
Shade the other side.
x-x
-y
3