# How do you find the slope of the line that is perpendicular to the line through (1, 9) and (10, 3 and 1/2)?

Aug 5, 2016

$\frac{18}{11}$

Find the slope of the line by dividing the change in the y values by the change in the x values. Then take the negative inverse of the slope of the line.

#### Explanation:

The slope equals the change in $y$ divided by the change in $x$, so

$y = 9 - 3 \frac{1}{2} = 5 \frac{1}{2}$

$x = 1 - 10 = - 9$

$\text{slope} = \frac{5 \frac{1}{2}}{- 9}$

Multiply $5 \frac{1}{2} \times 2 = 11$, then multiply $- 9 \times 2 = - 18$, so the slope of the line is

$\text{slope} = - \frac{11}{18}$

The negative inverse is $+ \frac{18}{11}$

So the slope of the line that is perpendicular to the line is $+ \frac{18}{11}$