Section 3.4 More About Slope 245 The line perpendicular to the given line has slope of - 3 2 . So, we graph this line by plotting the point (-2, 1) and then move down 3 units vertically and right 2 units horizontally to get to (0, -2). 4 (–2, 1) (0, –2) (3, 4) (0, 2) 2 4 –4 x y y = x + 2 23 Student Check 4 Graph the line that satisfies each condition. a. Graph the line 2x - y = -4 and the line that is parallel to it that passes through (2, -1). b. Graph the line y = 5x - 5 and the line that is perpendicular to it that passes through (5, 1). Troubleshooting Common Errors A common error associated with slope and parallel and perpendicular lines is shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. Are the lines y = 4x + 6 and 4x + y = 0 parallel, perpendicular, or neither? �������������������������������������� ���������������������������������������������������������������� The second equation is not in slope-intercept form. We must rewrite 4x + y = 0 in this form to identify its slope. 4x + y = 0 y = -4x The slope of y = 4x + 6 is m = 4. The slope of y = -4x is m = -4. The slopes are not the same, so the lines are not parallel. The slopes are not negative reciprocals of one another either, so the lines are not perpendicular. Objective 5 ▶ Troubleshoot common errors. The coefficient of equation is 4, so the slopes the lines are parallel. ANSWERS TO STUDENT CHECKS Student Check 1 a. The median annual income for women in 1990 was $27,645 and it increased by $1100 per year after 1990. Three points are (0, 27,645), (1, 28,745), and (2, 29,845). b. The initial value of the car was $15,000 and its value decreased by $2500 each year. Three points are (0, 15,000), (1, 12,500) and (2, 10,000) c. The cost of renting the car is $40 plus $0.50 per mile driven. Three points are (0, 40), (1, 40.50), and (2, 41). Student Check 2 a. 8 12 = 2 3 b. - 60 400 =- 3 20 c. - 5000 1 =-5000 Student Check 3 a. perpendicular b. neither c. parallel d. perpendicular each equa pes are the same and the l are
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