Determine whether the two given lines are perpendicular.
-3x - 8y = 18 48x + 12y = 18
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if the two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other. To find the slope of the first line, we can rearrange it in slope-intercept form:

3x - 8y = 18
-8y = -3x + 18
y = (3/8)x - 9/4

The slope of this line is 3/8.

To find the slope of the second line, we can also rearrange it in slope-intercept form:

48x + 12y = 18
12y = -48x + 18
y = (-4)x + 3/2

The slope of this line is -4.

The slopes are not negative reciprocals (they are not even fractions), so the lines are not perpendicular. The correct answer is B.

Determine Whether the Two Given Lines Are Perpendicular