Tell whether the lines are "parallel", "perpendicular", or "neither."
-$$\begin{array} { l }
3 x - 4 y = 1 \
8 x + 6 y = 1
\end{array}$$
A) Parallel
B) Neither
C) Perpendicular

Question

Tell whether the lines are "parallel", "perpendicular", or "neither."
-$$\begin{array} { l } 
3 x - 4 y = 1 \
8 x + 6 y = 1
\end{array}$$
A) Parallel
B) Neither
C) Perpendicular

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 is the slope. For the first equation, $3x - 4y = 1$, we solve for y to get $y = \frac{3}{4}x - \frac{1}{4}$. For the second equation, $8x + 6y = 1$, we solve for y to get $y = -\frac{4}{3}x + \frac{1}{6}$. The slopes are $\frac{3}{4}$ and $-\frac{4}{3}$, respectively. Since the product of the slopes is -1 ($\frac{3}{4} * -\frac{4}{3} = -1$), the lines are perpendicular.

Tell Whether the Lines Are "Parallel", "Perpendicular", or "Neither 3x−4y=18x+6y=1\begin{array} { l } 3 x - 4 y = 1 \\8 x + 6 y = 1\end{array}3x−4y=18x+6y=1​

Tell Whether the Lines Are "Parallel", "Perpendicular", or "Neither $\begin{array} { l } 3 x - 4 y = 1 \\8 x + 6 y = 1\end{array}$