YOU TRY 1 Shown here is the graph of 2x 3y 6. Find three points that solve 2x 3y 6, and fi nd three points that are not in the solution set. x y 5 5 5 5 2x 3y 6 2 Graph a Linear Inequality in Two Variables As you saw in the graph in Example 1, the line divides the plane into two regions or half planes. The line x y 1 is the boundary line between the two half planes. We can use this boundary and two different methods to graph a linear inequality in two variables. The fi rst method we will discuss is the test point method. Procedure Graphing a Linear Inequality in Two Variables Using the Test Point Method Step 1: Graph the boundary line. If the inequality contains or , make it a solid line. If the inequality contains or , make it a dotted line. Step 2: Choose a test point not on the line, and shade the appropriate region. Substitute the test point into the inequality. If (0, 0) is not on the line, it is an easy point to test in the inequality. a) If it makes the inequality true, shade the side of the line containing the test point. All points in the shaded region are part of the solution set. b) If the test point does not satisfy the inequality, shade the other side of the line. All points in the shaded region are part of the solution set. EXAMPLE 2 In-Class Example 2 Graph x y 2. Answer: x y x y 2 Graph 3x 2y 6. Solution Step 1: Graph the boundary line 3x 2y 6 as a solid line. x y 5 5 5 5 288 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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