Determine whether the lines are parallel, perpendicular, or neither.
-3x - 2y = -16 3x + 4y = 5
A)parallel
B)perpendicular
C)neither

Question

Quizplus · Accepted Answer

To determine whether the lines are parallel or perpendicular, we need to put them in slope-intercept form (y = mx + b) where the coefficient of x is the slope of the line.

3x - 2y = -16 
-2y = -3x - 16 
y = (3/2)x + 8

3x + 4y = 5 
4y = -3x + 5 
y = (-3/4)x + (5/4)

The slopes of the lines are (3/2) and (-3/4). They are not equal, nor are they opposite reciprocals. Therefore, the lines are neither parallel nor perpendicular. To determine if the lines are parallel or perpendicular, we need to compare their slopes. We can rewrite each equation in slope-intercept form (y = mx + b) to find their slopes:

3x - 2y = -16 
-2y = -3x - 16 
y = (3/2)x + 8

3x + 4y = 5 
4y = -3x + 5 
y = (-3/4)x + (5/4)

The slope of the first line is 3/2 and the slope of the second line is -3/4. Since these slopes are not the same (and not negative reciprocals of each other), the lines are neither parallel nor perpendicular. Therefore, the answer is C.

Determine Whether the Lines Are Parallel, Perpendicular, or Neither