Determine whether the lines are parallel, perpendicular, or neither.
-$$\begin{array} { l }
4 x + 2 y = 2 \
2 x - 4 y = 8
\end{array}$$
A) Parallel
B) Perpendicular
C) Neither

Question

Determine whether the lines are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
4 x + 2 y = 2 \
2 x - 4 y = 8
\end{array}$$
A) Parallel
B) Perpendicular
C) Neither

Quizplus · Accepted Answer

To determine the relationship between the two lines, we first convert the equations into slope-intercept form (y = mx + b), where m represents the slope. For the first equation, $4x + 2y = 2$, we solve for y: $2y = -4x + 2$, so $y = -2x + 1$, giving a slope of -2. For the second equation, $2x - 4y = 8$, we solve for y: $-4y = -2x + 8$, so $y = \frac{1}{2}x - 2$, giving a slope of $\frac{1}{2}$. Since the slopes are negative reciprocals of each other ($-2$ and $\frac{1}{2}$), the lines are perpendicular.

Determine Whether the Lines Are Parallel, Perpendicular, or Neither 4x+2y=22x−4y=8\begin{array} { l } 4 x + 2 y = 2 \\2 x - 4 y = 8\end{array}4x+2y=22x−4y=8​

Determine Whether the Lines Are Parallel, Perpendicular, or Neither $\begin{array} { l } 4 x + 2 y = 2 \\2 x - 4 y = 8\end{array}$