Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.

Question

y = -2/3x + 1
2x – 3y = –3

A. Parallel
B. Perpendicular
C. Neither

Answer 1

To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes.

The first equation is in the slope-intercept form, y = mx + b, where m is the slope. In this case, the slope of the first equation is -2/3.

To write the second equation in slope-intercept form, we can solve it for y:
2x - 3y = -3
-3y = -2x - 3
y = (2/3)x + 1

The slope of the second equation is 2/3.

Since the slopes of the two lines are negative reciprocals of each other, (-2/3) and (2/3), the lines are perpendicular.

Therefore, the answer is B. Perpendicular.