Procedure Graph a Linear Inequality in Two Variables Using the Slope-Intercept Method 1) Write the inequality in the form y mx b (y mx b) or y mx b (y mx b), and graph the boundary line y mx b. 2) If the inequality is in the form y mx b or y mx b, shade above the line. 3) If the inequality is in the form y mx b or y mx b, shade below the line. EXAMPLE 3 Graph each inequality using the slope-intercept method. a) y 1 3 x 5 b) 2x y 2 Solution a) The inequality y 1 3 x 5 is already in slope-intercept form. Graph the boundary line y 1 3 x 5 as a dotted line. Since y 1 3 x 5 has a less than symbol, shade below the line. All points in the shaded region satisfy y 1 3 x 5. We can choose a point such as (0, 0) in the shaded region as a check. Substituting this point into y 1 3 x 5 gives us 0 1 3 (0) 5, or 0 5, which is true. b) Solve 2x y 2 for y. 2x y 2 y 2x 2 Subtract 2x. y 2x 2 y 5 y x 5 13 5 5 5 Divide by 1, and change the direction of the inequality symbol. Graph y 2x 2 as a solid line. Since y 2x 2 has a greater than or equal to symbol, shade above the line. All points on the line and in the shaded region satisfy 2x y 2. x x y 5 2x y 2 5 5 5 190 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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