Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l }
- 5 x - 4 y = 6 \
\frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 8
\end{array}$$
A) neither
B) perpendicular
C) parallel

Question

Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
- 5 x - 4 y = 6 \
\frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 8
\end{array}$$
A) neither
B) perpendicular
C) parallel

Quizplus · Accepted Answer

To determine the relationship between the two lines, we need to find their slopes. For the first equation, we can rewrite it in slope-intercept form (y = mx + b) to find the slope: $$-5x - 4y = 6 \Rightarrow -4y = 5x + 6 \Rightarrow y = -\frac{5}{4}x - \frac{3}{2}$$. So, the slope of the first line is $-\frac{5}{4}$. For the second equation, we can do the same: $$\frac{1}{2}x + \frac{2}{3}y = 8 \Rightarrow \frac{2}{3}y = -\frac{1}{2}x + 8 \Rightarrow y = -\frac{3}{4}x + 12$$. So, the slope of the second line is $-\frac{3}{4}$. Since the slopes are different and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Determine If the Lines Defined by the Given Equations Are −5x−4y=612x+23y=8\begin{array} { l } - 5 x - 4 y = 6 \\\frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 8\end{array}−5x−4y=621​x+32​y=8​

Determine If the Lines Defined by the Given Equations Are $\begin{array} { l } - 5 x - 4 y = 6 \\\frac { 1 } { 2 } x + \frac { 2 } { 3 } y = 8\end{array}$