Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l }
- 4 y = - 3 x - 3 \
- 12 x = 9 y + 8
\end{array}$$
A) parallel
B) perpendicular
C) neither

Question

Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
- 4 y = - 3 x - 3 \
- 12 x = 9 y + 8
\end{array}$$
A) parallel
B) perpendicular
C) neither

Quizplus · Accepted Answer

To determine if the lines are parallel, perpendicular, or neither, we need to find the slopes of each line. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. For the first equation, $-4y = -3x - 3$, we can rewrite it as $y = \frac{3}{4}x + \frac{3}{4}$. For the second equation, $-12x = 9y + 8$, we can rewrite it as $y = -\frac{4}{3}x - \frac{8}{9}$. The slopes are $\frac{3}{4}$ and $-\frac{4}{3}$, respectively. Since the product of the slopes is $\frac{3}{4} \times -\frac{4}{3} = -1$, the lines are perpendicular.

Determine If the Lines Defined by the Given Equations Are −4y=−3x−3−12x=9y+8\begin{array} { l } - 4 y = - 3 x - 3 \\- 12 x = 9 y + 8\end{array}−4y=−3x−3−12x=9y+8​

Determine If the Lines Defined by the Given Equations Are $\begin{array} { l } - 4 y = - 3 x - 3 \\- 12 x = 9 y + 8\end{array}$