1. GOAL Graphing linear inequalities in two variables

2. REMEMBER THE SYMBOLS Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

3. LINEAR INEQUALITIES An example of a linear inequality in two variables is x - 3y ≤ 6. The solution of an inequality in two variables, x and y, is an ordered pair (x, y) that produces a true statement when substituted into the inequality. Which ordered pair is NOT a solution of x - 3y ≤ 6? A. (0,0) B. (6,-1) C. (10, 3) D. (-1,2) x - 3y ≤ 6 Substitute each point into the inequality. If the statement is true then it is a solution. (0) – 3(0) ≤ 6 True, therefore (0,0) is a solution.

4. 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. There is a BOUNDARY LINE that divides the coordinate plane into two HALF-PLANES. Only one half-plane contains the points that represent the solutions to the inequality.

5. GRAPHING LINEAR INEQUALITIES Graphing Boundary Lines : Use a dashed line for. Use a solid line for ≤ or ≥.

6. 6 To graph the solution set for a linear inequality: 2. Select a test point, not on the boundary line, usually the origin, (0,0) and determine if it is a solution. 3. Shade a half-plane. 1. Graph the boundary line. GRAPHING AN INEQUALITY

7. 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.

8. 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.

9. 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.

10. 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.

11. GRAPH AN INEQUALITY Graph the equation STEP 1 Graph the inequality x. Graph the inequality x ≤ -1. STEP 2 Test (3,0) 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 does not contain the point (3,0), because (3,0) is not a solution to the inequality.