# What is the slope of any line perpendicular to the line passing through (16,6) and (-2,-13)?

Apr 3, 2018

$- \frac{18}{19}$

#### Explanation:

Let's first find the slope of the line passing through the aforementioned points

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \rightarrow$ Finding a slope via two points formula

$\frac{- 13 - 6}{- 2 - 16} \rightarrow$ Plug in the points

$\frac{- 19}{-} 18$

$\frac{19}{18} \rightarrow$ This is the slope of the line

Perpendicular slopes are opposite reciprocals of each other

To make something the opposite of another number, add a negative sign in front of it (a positive number's opposite will be negative, a negative number's opposite will be positive)

To find the reciprocal of a number, switch the numerator and denominator

$\frac{19}{18}$

$- \frac{19}{18} \rightarrow$ The opposite

$- \frac{18}{19} \rightarrow$ The (opposite) reciprocal