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2.8 Graphing Linear Inequalities Algebra 2 Mrs. Spitz Fall 2006 Objectives • Draw graphs of inequalities in two variables, and • Write an inequality to solve problems. Assignment • pp. 94-95#13-28 all Introduction • When graphing inequalities, the boundaries you draw may be solid or dashed. If the inequality uses the symbol ≥ or ≤ , which may include equality, the boundary will be solid. Otherwise, it will be dashed. After graphing the boundary, you must determine which region is to be shaded. Introduction • Test a point on one side of the line. If the ordered pair satisfied the inequality, that region contains solutions to the inequality. If the ordered pair does not satisfy the inequality, the other region is the solution. Chalkboard examples 1. Graph y < 3. 2. Graph y ≤ |x| Chalkboard examples 1. Graph 1 3 y x 4 4 2. Graph y < 3x +1 Chalkboard examples 1. Graph y ≥ |x| + 1 2. Graph 3x ≥ 4y Ex. 1: Graph 2y – 5 ≤ 8. • The boundary will be the graph of 2y – 5 = 8. Use x and y intercepts to graph the boundary more easily. x-intercept y-intercept 2 y 5x 8 2 y 5x 8 2(0) 5 x 8 2 y 5(0) 8 2y 8 5x 8 x 8 5 y4 Graph the x and y intercepts on a coordinate graphing plane. Draw a solid line connecting these two intercepts. This is the boundary. Now graph/shade • Now test a point. • Try (2,0) 2 y 5x 8 2(0) 5(2) 8 0 10 8 10 8 The region that contains (2, 0) should be shaded. Ex. 2: Graph y > |x| - 1. • The absolute value has two conditions to consider • y > -x – 1 When x < 0 When x ≥ 0 y > -x -1 y > x -1 Graph each inequality for the specified values of x. The lines will be dashed. Now graph/shade • Now test a point. • Try (0,0) y | x | 1 0 | 0 | 1 0 1 The region that contains (0, 0) should be shaded.