Solve the problem.
-Line $L _ { 1 }$ has the equation $8 x - 16 y = 1$. Line $L _ { 2 }$ passes through the points $( 1,5 )$ and $( 2,7 )$. Determine whether these lines are parallel, perpendicular, or neither.
A) Parallel
B) Perpendicular
C) Neither

Question

Quizplus · Accepted Answer

The slope of $L_1$ can be found by rearranging its equation into slope-intercept form $y = mx + b$, where $m$ is the slope. For $L_1$, $8x - 16y = 1$ becomes $y = \frac{1}{2}x - \frac{1}{16}$, so its slope is $\frac{1}{2}$. The slope of $L_2$ can be found using the two points it passes through, using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For $L_2$, using points $(1,5)$ and $(2,7)$, the slope is $m = \frac{7 - 5}{2 - 1} = 2$. Since the slopes of $L_1$ and $L_2$ are neither equal (which would indicate parallel lines) nor negative reciprocals of each other (which would indicate perpendicular lines), the lines are neither parallel nor perpendicular.

Solve the Problem L1L _ { 1 }L1​ Has the Equation 8x−16y=18 x - 16 y = 18x−16y=1

Solve the Problem $L _ { 1 }$ Has the Equation $8 x - 16 y = 1$