1. Dr. Fowler CCM Graphing Linear Inequalities

2. 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. Graph an Inequality in Two Variables

3. Graphing Linear Inequalities The boundary line will be a: –Solid line when ≤ and ≥ are used. –Dashed line when are used. shaded 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. –Use a solid line for ≤ or ≥.

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

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

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

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

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

10. Excellent Job !!! Well Done

11. Stop Notes Do Worksheet