# What is the slope of any line perpendicular to the line passing through (4,2) and (-1,10)?

Oct 20, 2017

$\frac{5}{8}$

#### Explanation:

First figure out the slope of the line that passes through those points using the slope formula:

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ where ${y}_{2} = 10 , {y}_{1} = 2 \mathmr{and} {x}_{2} = - 1 , {x}_{1} = 4$

So:

$\frac{10 - 2}{- 1 - 4} = \frac{8}{-} 5 =$slope

NOTE: You could also let ${y}_{2} = 2 , {y}_{1} - 10 \mathmr{and} {x}_{2} = 4 , {x}_{1} = - 1$
Which leads to the same answer (thanks Tony B.!):

$\frac{2 - 10}{4 - \left(- 1\right)} = \frac{- 8}{5} =$slope

Perpendicular lines always have different signed slopes (meaning if one line's slope is positive, the perpendicular line's slope is negative and similarly negative $\to$ positive). Thus our slope is positive.

Also perpendicular lines are reciprocals of each other so our new slope is:

$\frac{5}{8}$