Note If the inequality had been x y 3, then the line would have been drawn as a dotted line and all points on the line would not be part of the solution set. As we saw in the preceding graph, the line divides the plane into two regions or half planes. The line x y 3 is the boundary line between the two half planes. We will use this boundary line to graph a linear inequality in two variables. Notice that the boundary line is written as an equation; it uses an equal sign. EXAMPLE 1 Graph 3x 4y 8. If the inequality includes the equals condition, the boundary line is drawn solid. Points on this line make the inequality true. Procedure Graph a Linear Inequality in Two Variables Using a Test Point 1) Graph the boundary line. If the inequality contains or , make this boundary line solid. If the inequality contains or , make it dotted. 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 region 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 region on the other side of the line. All points in the shaded region are part of the solution set. Solution 1) Graph the boundary line 3x 4y 8 as a solid line. 2) Choose a test point not on the line and substitute it into the inequality to determine whether it makes the inequality true. x y 5 Test point (0, 0) 5 5 5 Test Point Substitute into 3x 4y 8 (0, 0) 3(0) 4(0) 8 0 8 False 188 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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