Determine whether the lines are parallel, perpendicular, or neither.
-3x - 4y = -18 8x + 6y = -1
A)perpendicular
B)neither
C)parallel

Question

Quizplus · Accepted Answer

Both equations can be rewritten in slope-intercept form (y = mx + b):
- 3x + 4y = -18 --> y = (3/4)x - 9/2
- 8x + 6y = -1 --> y = (-4/3)x - 1/6

The slopes of the two lines are:
- m1 = 3/4
- m2 = -4/3

To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes:

- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals, the lines are perpendicular.
- Otherwise, the lines are neither parallel nor perpendicular.

In this case, m1 * m2 = (3/4) * (-4/3) = -1, which means the lines are perpendicular. Therefore, the answer is A) perpendicular.

Determine Whether the Lines Are Parallel, Perpendicular, or Neither