Determine whether the pair of lines is parallel, perpendicular, or neither.
-$\begin{array} { l }
3 x - 2 y = 17 \
2 x + 3 y = 12
\end{array}$
A) parallel
B) perpendicular
C) neither

Question

Determine whether the pair of lines is parallel, perpendicular, or neither.
-$\begin{array} { l } 
3 x - 2 y = 17 \
2 x + 3 y = 12
\end{array}$
A) parallel
B) perpendicular
C) neither

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 = 17 becomes -2y = -3x + 17, then y = (3/2)x - 17/2. For the second equation, 2x + 3y = 12 becomes 3y = -2x + 12, then y = (-2/3)x + 4. The slopes are 3/2 and -2/3, respectively. Since the product of the slopes is -1 (3/2 * -2/3 = -1), the lines are perpendicular.

Determine Whether the Pair of Lines Is Parallel, Perpendicular, or Neither