Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. $$\begin{array} { l }
2 y = 9 x - 3 \
8 x = 7 y + 4
\end{array}$$
A) parallel
B) perpendicular
C) neither

Question

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. $$\begin{array} { l } 
2 y = 9 x - 3 \
8 x = 7 y + 4
\end{array}$$
A) parallel
B) perpendicular
C) neither

Quizplus · Accepted Answer

To determine the relationship between the two lines, we need to convert their equations into slope-intercept form (y = mx + b), where m is the slope. For the first equation, $2y = 9x - 3$, dividing by 2 gives $y = \frac{9}{2}x - \frac{3}{2}$. For the second equation, $8x = 7y + 4$, rearranging gives $7y = 8x - 4$, and dividing by 7 gives $y = \frac{8}{7}x - \frac{4}{7}$. The slopes are $\frac{9}{2}$ and $\frac{8}{7}$, which are neither equal (not parallel) nor negative reciprocals of each other (not perpendicular).

Determine If the Lines Are Parallel, Perpendicular, or Neither Parallel 2y=9x−38x=7y+4\begin{array} { l } 2 y = 9 x - 3 \\8 x = 7 y + 4\end{array}2y=9x−38x=7y+4​

Determine If the Lines Are Parallel, Perpendicular, or Neither Parallel $\begin{array} { l } 2 y = 9 x - 3 \\8 x = 7 y + 4\end{array}$