Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.
-$( 3 , - 4 )$ and $( 5,10 )$
A) (a) 7; (b) $- 7$
B) (a) $7 ; ($ b $) - \frac { 1 } { 7 }$
C) (a) $\frac { 1 } { 7 }$;
(b) $- 7$
D) (a) $- 7 ;$ (b) $\frac { 1 } { 7 }$

Question

Quizplus · Accepted Answer

The slope of the line passing through the points $(3, -4)$ and $(5, 10)$ is calculated using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, we get $m = \frac{10 - (-4)}{5 - 3} = \frac{14}{2} = 7$. Lines parallel to this line will have the same slope, so $m_{parallel} = 7$. Lines perpendicular to this line will have a slope that is the negative reciprocal of $7$, so $m_{perpendicular} = -\frac{1}{7}$.

Find the Slopes of the Lines That Are (A) Parallel (3,−4)( 3 , - 4 )(3,−4)

Find the Slopes of the Lines That Are (A) Parallel $( 3 , - 4 )$