Objective Graph Linear Equations and Linear Inequalities in

Objective Graph Linear Equations and Linear Inequalities in Two Variables

Section 7. 8 “Graph Linear Inequalities” Linear Inequalitiesthe result of replacing the = sign in a linear equation with an inequality sign.

Linear Inequalities An example of a linear inequality in two variables is x - 3 y ≤ 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 - 3 y ≤ 6? A. (0, 0) B. (6, -1) C. (10, 3) D. (-1, 2) Substitute each point into the inequality. If the statement is true then it is a solution. x - 3 y ≤ 6 (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. 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.

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

Graph an Inequality Graph the inequality STEP 1 Graph the equation STEP 2 Test (0, 0) in the original inequality. y > 4 x - 3. 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 inequality STEP 1 Graph the equation STEP 2 Test (1, 0) in the original inequality. x + 2 y ≤ 0. 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 inequality STEP 1 Graph the equation STEP 2 Test (1, 0) in the original inequality. x + 3 y ≥ -1. 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 inequality STEP 1 Graph the equation STEP 2 Test (2, 0) in the original inequality. Use only the ycoordinate, because the inequality does not have a x-variable. y ≥ -3. 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 inequality STEP 1 Graph the equation STEP 2 Test (3, 0) in the original inequality. Use only the ycoordinate, because the inequality does not have a x-variable. x ≤ -1. STEP 3 Shade the half-plane that does not contain the point (3, 0), because (3, 0) is not a solution to the inequality.

Challenge “Can You Write and Graph the Mystery Inequality? ? ? ” The points (2, 5) and (-3, -5) lie on the boundary line. The points (6, 5) and (-2, -3) are solutions of the inequality. y ≤ 2 x + 1

Graph Absolute Value Functions Extension Activity 6. 5 ABSOLUTE VALUE FUNCTIONg(x) = |x -3| f(x) = |x| x f(x)=|x| -5 5 -2 g(x) = |x - 3| x g(x)=|x-3| -3 6 2 0 3 0 1 1 4 1 3 3 6 3 f(x) = |x|