# What is the equation of the line perpendicular to  y=-2/5x-1  at x=-1 ?

Apr 11, 2017

$10 y = 25 x + 19$

#### Explanation:

given that $y = - \frac{2}{5} x - 1$

at $x = - 1$
$y = - \frac{2}{5} \left(- 1\right) - 1 = \frac{2}{5} - 1 = - \frac{3}{5}$

the line perpendicular has a slope, m where

$m \cdot \left(- \frac{2}{5}\right) = - 1$ $\to m = \frac{5}{2}$

the equation is,

$y = m x + c$ and plug in the values of $x , y \mathmr{and} m$ to find $c$

$- \frac{3}{5} = \frac{5}{2} \cdot \left(- 1\right) + c$

$- \frac{3}{5} = - \frac{5}{2} + c$

$- \frac{3}{5} + \frac{5}{2} = c$ $\to \frac{19}{10}$

therefore the equation is $y = \frac{5}{2} x + \frac{19}{10}$ $\to 10 y = 25 x + 19$