Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
-$3 x-2 y=-8$
$2 x+3 y=-8$
A) Neither
B) Perpendicular
C) Parallel

Question

Quizplus · Accepted Answer

The slopes of the lines are found by rearranging each equation into slope-intercept form (y = mx + b). For the first equation, $3x - 2y = -8$, rearranging gives $y = \frac{3}{2}x + 4$, so the slope is $\frac{3}{2}$. For the second equation, $2x + 3y = -8$, rearranging gives $y = -\frac{2}{3}x - \frac{8}{3}$, so the slope is $-\frac{2}{3}$. Since the slopes are negative reciprocals of each other ($\frac{3}{2}$ and $-\frac{2}{3}$), the lines are perpendicular.

Determine Whether the Graphs of the Equations Are Parallel Lines 3x−2y=−83 x-2 y=-83x−2y=−8

Determine Whether the Graphs of the Equations Are Parallel Lines $3 x-2 y=-8$