# What is the equation of the line perpendicular to y=-22/3x  that passes through  (-1,9) ?

Dec 3, 2015

$y = \frac{3}{22} x + \frac{201}{22}$

#### Explanation:

Two lines with slopes ${m}_{1}$ and ${m}_{2}$ are perpendicular if ${m}_{1} = - \frac{1}{m} _ 2$

So, since the slope of $y = - \frac{22}{3} x$ is $- \frac{22}{3}$, the perpendicular slope is $\frac{3}{22}$.

Once we know the slope and a point $\left({x}_{0} , {y}_{0}\right)$ the equation for the line with that slope passing through that point is

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

$y - 9 = \frac{3}{22} \left(x + 1\right)$
$y = \frac{3}{22} x + \frac{3}{22} + 9 = \frac{3}{22} x + \frac{201}{22}$
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