# What is the equation of the line perpendicular to y=9/10x  that passes through  (-1,5) ?

Jan 4, 2016

$y = - \frac{10}{9} x + \frac{35}{9}$.

#### Explanation:

A straight line graph of form $y = m x + c$ has gradient $m$ and y-intercept $c$.

Perpendicular lines have gradients whose product is $- 1$.

So the gradient of the given line is $\frac{9}{10}$ and so a line perpendicular to this line would have gradient $- \frac{10}{9}$.

We may now substitute the point $\left(x , y\right) = \left(- 1 , 5\right)$ into the general equation of the required line to solve :

$y = m x + c$

$\therefore 5 = \frac{- 10}{9} \left(- 1\right) + c$

$\therefore c = \frac{35}{9}$.

Thus the required line has equation $y = - \frac{10}{9} x + \frac{35}{9}$.