Question

Find the slope of the line that is ​(a) parallel and ​(b) perpendicular to the line through the pair of points.​ (−2​,−7​) and ​(8​,4​)

Answer 1

Hey there! 

First, find the slope of the actual original pair of points.
The slope formula is:

$m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }$

So now, substitute the points in, whichever order you substitute the points into the equation doesn't matter, as long as the ones substituted in with the same subscript number.

$m = \frac{ -7 - 4 }{ -2 - 8 }$\

Once you subtract, you get:

$m = \frac{-11 }{ -10 }$

So the slope is 11/10.

A line that is parallel to another has the exact same slope that that another line has.

So therefore the line that is parallel has a slope of 11/10.

Perpendicular is another story. You take the reciprocal of the slope of the other line, and then change the sign before it: ex: negative would become positive.

So therefore the line that is perpendicular has a slope of -10/11.