Decide whether the pair of lines is parallel, perpendicular, or neither.
-3x - 2y = 14 2x + 3y = -4
A)parallel
B)perpendicular
C)neither

Question

Quizplus · Accepted Answer

To determine the relationship between the two lines, we first convert the equations into slope-intercept form (y = mx + b), where m represents the slope. For the first equation, 3x - 2y = 14, rearranging for y gives y = (3/2)x - 7. Thus, the slope (m1) is 3/2. For the second equation, 2x + 3y = -4, rearranging for y gives y = -(2/3)x - 4/3. Thus, the slope (m2) is -2/3. Since the slopes are negative reciprocals of each other (m1 = 3/2 and m2 = -2/3), the lines are perpendicular.

Decide Whether the Pair of Lines Is Parallel, Perpendicular, or Neither