Section 3.4 More About Slope 243 �� ������������������������ ������������������ Determine if the lines are parallel, perpendicular, or neither. 3a. y = x + 4 and y = -x - 3 3b. y = 2x + 3 and y = 1 2 x - 4 3c. 2x + y = 4 and 4x + 2y = 6 3d. 4x - y = 8 and x + 4y = -4 Solutions 3a. Both equations are in slope-intercept form. The slope of y = x + 4 is m = 1. The slope of y = -x + 3 is m = -1. The slopes are not the same, so the lines are not parallel. The slopes, however, are negative reciprocals of one another since 1=-a 1 -1 b. So, the lines are perpendicular. 3b. Both equations are in slope-intercept form. The slope of y = 2x + 3 is m = 2. The slope of y = 1 2 x - 4 is m = 1 2 . The slopes are not the same, so the lines are not parallel. The slopes are reciprocals but not opposites. Therefore, the lines are not perpendicular to one another. So, the lines are neither parallel nor perpendicular. 3c. We must first write each equation in slope-intercept form. 2x + y = 4 2x + y - 2x = 4 - 2x y = -2x + 4 m = -2 4x + 2y = 6 4x + 2y - 4x = 6 - 4x 2y=-4x + 6 2y 2 = -4x + 6 2 y = -2x + 3 m=-2 The slope of each line is m = -2. The lines have different y-intercepts. Therefore, the lines are parallel. 3d. We must first write each equation in slope-intercept form. 4x - y = 8 4x - y - 4x = 8 - 4x -y = -4x + 8 -1(-y) = -1(-4x + 8) y = 4x - 8 m = 4 x + 4y = -4 x + 4y - x = -4 - x 4y = -x - 4 4y 4 = -x - 4 4 y = - 1 4 x - 1 m=- 1 4 The slopes of the lines are negative reciprocals of one another, so the lines are perpendicular. Student Check 3 Determine if the lines are parallel, perpendicular, or neither. a. y=-5x - 1 and y = 1 5 x + 2 b. y = 3x - 4 and y = -3x + 5 c. 3x + 2y = 6 and 9x + 6y = 10 d. 2x + 3y = 6 and 3x - 2y = 12
hendricks_beginning_algebra_1e_ch1_3
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