1. Graphing Linear Inequalities
Dr. Fowler  CCM
Graphing Linear Inequalities

2. Graph an Inequality in Two Variables
The graph of an inequality in two variables is the set of points that represent all solutions of the inequality.
The BOUNDARY LINE of a linear inequality divides the coordinate plane into two HALF-PLANES. Only one half-plane contains the points that represent the solutions to the inequality.

3. Graphing Linear Inequalities
The boundary line will be a:
Solid line when ≤ and ≥ are used.
Dashed line when < and > are used.
Our graph will be shaded on one side of the boundary line to show where the solutions of the inequality are located.

4. Graphing Linear Inequalities
Graphing Boundary Lines:
Use a dashed line for < or >.
Use a solid line for ≤ or ≥.

5. Graph the inequality y > 4x - 3.
Graph an Inequality
Graph the inequality y > 4x - 3.
STEP 2
STEP 3
STEP 1
Graph the equation
Test (0,0) in the original inequality.
Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality.

6. Graph the inequality x + 2y ≤ 0.
Graph an Inequality
Graph the inequality x + 2y ≤ 0.
STEP 2
STEP 3
STEP 1
Shade the half-plane that does not contain the point (1,0), because (1,0) is not a solution to the inequality.
Graph the equation
Test (1,0) in the original inequality.
2y = -x
__ __
2 2
y = -1 x __ 2

7. Graph the inequality x + 3y ≥ -1.
Graph an Inequality
Graph the inequality x + 3y ≥ -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality.
Graph the equation
Test (1,0) in the original inequality.
Plug in Zero’s to find x & y intercepts:
X intercept = -1
Y intercept = -1/3

8. Graph the inequality y ≥ -3.
Graph an Inequality
Graph the inequality y ≥ -3.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality.
Graph the equation
Test (2,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.
X intercept = none
Y intercept = -3

9. Graph the inequality x ≤ -1.
Graph an Inequality
Graph the inequality x ≤ -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that does not contain the point (0,3), because (0,3) is not a solution to the inequality.
Graph the equation
Test (0,3) in the original inequality. Use only the x-coordinate, because the inequality does not have a y-variable.
y intercept = none
x intercept = -1
● 0,3

10. Excellent Job !!! Well Done

11. Stop Notes
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