Decide whether the pair of lines is parallel, perpendicular, or neither.
-$$\begin{array} { l }
9 x + 3 y = 12 \
15 x + 5 y = 22
\end{array}$$
A) parallel
B) perpendicular
C) neither

Question

Decide whether the pair of lines is parallel, perpendicular, or neither.
-$$\begin{array} { l } 
9 x + 3 y = 12 \
15 x + 5 y = 22
\end{array}$$
A) parallel
B) perpendicular
C) neither

Quizplus · Accepted Answer

To determine if the lines are parallel, perpendicular, or neither, we can compare their slopes. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. For the first equation, $9x + 3y = 12$, we can solve for $y$ to get the slope: $3y = -9x + 12$, so $y = -3x + 4$, which means the slope is $-3$. For the second equation, $15x + 5y = 22$, solving for $y$ gives: $5y = -15x + 22$, so $y = -3x + \frac{22}{5}$, which means the slope is also $-3$. Since both lines have the same slope, they are parallel.

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