GOAL Graphing linear inequalities in two variables

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

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.

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.

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

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

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.

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.

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.

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.

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.