Graphing Inequalities
Example: Graph the inequality
x – 3y < - 9
Step 1: Change the inequality sign (<) to an
equality sign(=):
x – 3y = -9 (Thi...
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...
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
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Graphing Inequalities Example

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Graphing Inequalities Example

  1. 1. Graphing Inequalities
  2. 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. 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. 4. -x x -y y 3 Plot the point (0,3)
  5. 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. 6. Step 4: Graph the line < > broken line ------------- y -x -y x -9 3
  7. 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. 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
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