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Algebra Part 3 Unit 7 Name____________________________ Date________________ Warm-up Solve the following absolute value equations and graph your solutions. 1. x−5 ≥7 2. x−4 ≤ 6 Guided Notes Unit 7 – Graph Linear Inequalities In Two Variables Review Graph the linear equations. 1) y = 2x – 3 2 2) y = − x + 1 3 3) 3x – 2y = 6 A linear inequality in two variables is a result of replacing the ______ sign in a linear equation with _____, _____, _____, _____. A solution of an inequality in two variables x and y, is an ordered pair ( , ) that produces a __________ statement where the values of x and y are ____________________ into the inequality. Is (8,3) a solution to x – y < 5? In a coordinate plane, the graph of an inequality in two variables is the set of points that represents ___________________ of the inequality. The _________________ __________ of a linear inequality divides the coordinate plane into ______ _________ ___________. Only one of the half-plane contains the points that represents the _______________ of the inequality. Key Concept: Graphing a Linear Inequality in Two Variables Step 1: Graph the boundary line. Use a dashed line line for ≥ or ≤. for < or > and use a solid Step 2: Shade above if the inequality symbol is ________ or _________. Shade below if the inequality symbol is _________ or ________. ***YOU CAN ONLY USE THE SHADING RULES ABOVE IF THE EQUATION IS IN SLOPE-INTERCEPT FORM!!! Examples Graph the inequality. 1) y > 4x – 3 2) y ≥ 3 x +3 4 3) y < 1 x+4 3 4) 3x – y > 2 7) x ≤ 2 Homework: Worksheet 5) 2x + 4y = -8 6) x + y = -4 8) y > -4