# What is the slope of any line perpendicular to the line passing through (3,8) and (20,-5)?

Apr 9, 2018

$\frac{17}{13}$

#### Explanation:

First let's find the slope of the line passing through the aforementioned points.

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \rightarrow$ Finding the slope using two points

$\frac{- 5 - 8}{20 - 3}$

$- \frac{13}{17} \rightarrow$ This is the slope

Perpendicular slopes are opposite reciprocals of one another.

Opposites: -2 and 2, 4 and -4, -18 and 18, etc.

Add a negative sign to the front of any number to find its negative.

$- \left(- \frac{13}{17}\right) = \frac{13}{17}$

To make something a reciprocal of another number, flip the numerator and denominator of the original number.

$\frac{13}{17} \rightarrow \frac{17}{13}$

Apr 9, 2018

$m = \frac{17}{13}$

#### Explanation:

First, find the slope of this line by using this formula:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Now you choose which point has ${y}_{2}$ and ${x}_{2}$ and which point has ${y}_{1}$ and ${x}_{1}$

${y}_{2} = 8$ and ${x}_{2} = 3$
${y}_{1} = - 5$ and ${x}_{1} = 20$

Now plug into the formula to get:

$m = \frac{8 - \left(- 5\right)}{3 - 20}$

$m = \frac{8 + 5}{3 - 20}$

$m = \frac{13}{- 17}$

$m = - \frac{13}{17}$

Now that we have found the slope of the first line we can find the slope of any line perpendicular to it. To do this you have to find the slope's opposite reciprocal. To do this just flip the fraction (change the numerator and denominator) and put a negative sign in front.

So the slope of any line perpendicular is

$m = \frac{17}{13}$