Determine whether the lines are parallel, perpendicular, or neither.
-$$\begin{array} { l }
28 x - 4 y = 7 \
7 x - y = 12
\end{array}$$
A) Parallel
B) Perpendicular
C) Neither

Question

Determine whether the lines are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
28 x - 4 y = 7 \
7 x - y = 12
\end{array}$$
A) Parallel
B) Perpendicular
C) Neither

Quizplus · Accepted Answer

To determine the relationship between the two lines, we need to compare their slopes. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. For the first equation, $28x - 4y = 7$, we can rearrange it to solve for $y$: $-4y = -28x + 7$, or $y = 7x - \frac{7}{4}$. The slope is $7$. For the second equation, $7x - y = 12$, rearranging gives $y = 7x - 12$, with the same slope of $7$. Since both lines have the same slope, they are parallel.

Determine Whether the Lines Are Parallel, Perpendicular, or Neither 28x−4y=77x−y=12\begin{array} { l } 28 x - 4 y = 7 \\7 x - y = 12\end{array}28x−4y=77x−y=12​

Determine Whether the Lines Are Parallel, Perpendicular, or Neither $\begin{array} { l } 28 x - 4 y = 7 \\7 x - y = 12\end{array}$