Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l }
- 4 x - 4 y = - 1 \
- \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = 3
\end{array}$$
A) perpendicular
B) parallel
C) neither

Question

Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
- 4 x - 4 y = - 1 \
- \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = 3
\end{array}$$
A) perpendicular
B) parallel
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, $-4x - 4y = -1$, we can rewrite it as $y = -x + \frac{1}{4}$, so the slope is $-1$. For the second equation, $-\frac{1}{2}x + \frac{1}{2}y = 3$, we can rewrite it as $y = x + 6$, so the slope is $1$. Since the slopes are negative reciprocals of each other ($-1$ and $1$), the lines are perpendicular.

Determine If the Lines Defined by the Given Equations Are −4x−4y=−1−12x+12y=3\begin{array} { l } - 4 x - 4 y = - 1 \\- \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = 3\end{array}−4x−4y=−1−21​x+21​y=3​

Determine If the Lines Defined by the Given Equations Are $\begin{array} { l } - 4 x - 4 y = - 1 \\- \frac { 1 } { 2 } x + \frac { 1 } { 2 } y = 3\end{array}$