Drill Explain how to graph the following line; y = 4x – 3

Objective SWBAT graph linear equations and linear inequalities in two variables

Section 6.7 “Graph Linear Inequalities” Section 6.7 “Graph Linear Inequalities” Linear Inequalities- the result of replacing the = sign the 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 - 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.

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 sections. Only one section contains the points that represent the solutions to the inequality. Graph an Inequality in Two Variables

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

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 towards the section 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 toward the section 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 toward the section 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 section 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 section 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 ≤ 2x + 1