YOU TRY 2 Graph each inequality. a) x 3y 1 b) x 2y 4 Another method we can use to graph linear inequalities in two variables involves writing the boundary line in slope-intercept form. Procedure Using Slope-Intercept Form to Graph a Linear Inequality in Two Variables Step 1: Write the inequality in the form y mx b (y mx b) or y mx b (y mx b). Step 2: Graph the boundary line y mx b. a) If the inequality contains or , make it a solid line. b) If the inequality contains or , make it a dotted line. Step 3: Shade the appropriate side of the line. a) If the inequality is in the form y mx b or y mx b, shade above the line. b) If the inequality is in the form y mx b or y mx b, shade below the line. Graph the inequality y 1 3 x 2 using the slope-intercept method. Solution a) Step 1: y 1 3 x 2 is already in the correct form. Step 2: Graph the boundary line y 1 3 x 2 as a dotted line. Step 3: Since y 1 3 x 2 has a less than symbol, shade below the line. All points in the shaded region satisfy y 1 3 x 2. We can choose a point, such as (0, 0), in the shaded region as a check. Substitute this point into the inequality. 0 1 3 (0) 2 0 0 2 0 2 True EXAMPLE 4 In-Class Example 4 Graph the inequality y 5 2 x 1 using the slope-intercept method. Answer: a) x y y x 2 x y y x 2 3 290 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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