Definition/Procedure Example 4.4 Linear and Compound Linear Inequalities in Two Variables A linear inequality in two variables is an inequality that can be written in the form Ax By C or Ax By C, where A, B, and C are real numbers and where A and B are not both zero. ( and may be substituted for and .) (p. 187) Graph a Linear Inequality in Two Variables Using a Test Point 1) Graph the boundary line. a) If the inequality contains or , make the boundary line solid. b) If the inequality contains or , make the boundary line 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. (p. 188) 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. (p. 190) www.mhhe.com/messersmith Some examples of linear inequalities in two variables are x 3y 2, y 2 3 x 5, y 1, x 4 Graph 2x y 3. 1) Graph the boundary line as a dotted line. 2) Choose a test point not on the line, and substitute it into the inequality to determine whether it makes the inequality true. Test Point Substitute into 2x y 3 (0, 0) 2(0) (0) 3 0 3 True Since the test point satisfi es the inequality, shade the region containing (0, 0). All points in the shaded region satisfy 2x y 3. 5 Graph x 3y 6 using the slope-intercept method. Write the inequality in slope-intercept form by solving x 3y 6 for y. x 3y 6 3y x 6 y 1 3 x 2 Graph y 1 3 x 2 as a solid line. Since y 1 3 x 2 has a symbol, shade below the line. All points on the line and in the shaded region satisfy x 3y 6. x y 5 5 5 t t 2x y x y 5 5 5 5 x 3y 6 CHAPTER 4 Summary 219
messersmith_power_intermediate_algebra_1e_ch4_7_10
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