Decide whether the pair of lines is parallel, perpendicular, or neither.
-$$\begin{array} { l }
3 \mathrm { x } - 6 \mathrm { y } = 7 \
18 \mathrm { x } + 9 \mathrm { y } = - 7
\end{array}$$
A) parallel
B) perpendicular
C) neither

Question

Decide whether the pair of lines is parallel, perpendicular, or neither.
-$$\begin{array} { l } 
3 \mathrm { x } - 6 \mathrm { y } = 7 \
18 \mathrm { x } + 9 \mathrm { y } = - 7
\end{array}$$
A) parallel
B) perpendicular
C) neither

Quizplus · Accepted Answer

To determine the relationship between the two lines, we first need to find their slopes. For the first equation, $3x - 6y = 7$, we can rewrite it in slope-intercept form ($y = mx + b$) to find the slope $m$. Doing so, we get $y = \frac{1}{2}x - \frac{7}{6}$, so the slope is $\frac{1}{2}$. For the second equation, $18x + 9y = -7$, we also rewrite it in slope-intercept form to get $y = -2x - \frac{7}{9}$, so the slope is $-2$. Since the slopes are negative reciprocals of each other ($\frac{1}{2}$ and $-2$), the lines are perpendicular.

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