Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. $$\begin{array} { l }
6 x + 4 y = 5 \
- \frac { 1 } { 2 } x + \frac { 3 } { 4 } y = - 2
\end{array}$$
A) parallel
B) neither
C) perpendicular

Question

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. $$\begin{array} { l } 
6 x + 4 y = 5 \
- \frac { 1 } { 2 } x + \frac { 3 } { 4 } y = - 2
\end{array}$$
A) parallel
B) neither
C) perpendicular

Quizplus · Accepted Answer

To determine the relationship between the two lines, we first convert their equations into slope-intercept form (y = mx + b), where m represents the slope. For the first equation, $6x + 4y = 5$, we solve for y to get $y = -\frac{3}{2}x + \frac{5}{4}$, so the slope is $-\frac{3}{2}$. For the second equation, $-\frac{1}{2}x + \frac{3}{4}y = -2$, we solve for y to get $y = \frac{2}{3}x - \frac{8}{3}$, so the slope is $\frac{2}{3}$. Since the slopes are negative reciprocals of each other ($-\frac{3}{2}$ and $\frac{2}{3}$), the lines are perpendicular.

Determine If the Lines Are Parallel, Perpendicular, or Neither Parallel 6x+4y=5−12x+34y=−2\begin{array} { l } 6 x + 4 y = 5 \\- \frac { 1 } { 2 } x + \frac { 3 } { 4 } y = - 2\end{array}6x+4y=5−21​x+43​y=−2​

Determine If the Lines Are Parallel, Perpendicular, or Neither Parallel $\begin{array} { l } 6 x + 4 y = 5 \\- \frac { 1 } { 2 } x + \frac { 3 } { 4 } y = - 2\end{array}$