# What is the equation of the line that passes through the origin and is perpendicular to the line that passes through the following points: (9,2),(-2,8) ?

Jun 4, 2016

$6 y = 11 x$

#### Explanation:

A line through $\left(9 , 2\right)$ and $\left(- 2 , 8\right)$ has a slope of
$\textcolor{w h i t e}{\text{XXX}} {m}_{1} = \frac{8 - 2}{- 2 - 9} = - \frac{6}{11}$

All lines perpendicular to this will have a slope of
$\textcolor{w h i t e}{\text{XXX}} {m}_{2} = - \frac{1}{m} _ 1 = \frac{11}{6}$

Using the slope-point form, a line through the origin with this perpendicular slope will have an equation:
$\textcolor{w h i t e}{\text{XXX}} \frac{y - 0}{x - 0} = \frac{11}{6}$
or
$\textcolor{w h i t e}{\text{XXX}} 6 y = 11 x$