Tell whether the lines are "parallel", "perpendicular", or "neither."
-3x - 8y = 9 32x + 12y = 9
A) Parallel
B) Neither
C) Perpendicular

Question

Quizplus · Accepted Answer

To determine the relationship between two lines, we can compare their slopes. The slope-intercept form of a line is y = mx + b, where m is the slope. For the first equation, 3x - 8y = 9, we can rearrange it to solve for y: 8y = 3x - 9, so y = (3/8)x - 9/8. The slope of this line is 3/8. For the second equation, 32x + 12y = 9, rearranging gives 12y = -32x + 9, so y = (-32/12)x + 9/12, simplifying to y = (-8/3)x + 3/4. The slope of this line is -8/3. Two lines are perpendicular if the product of their slopes is -1. Multiplying the slopes (3/8) * (-8/3) gives -1, so the lines are perpendicular.

Tell Whether the Lines Are "Parallel", "Perpendicular", or "Neither