# What is the standard form of a line that goes through (5, -4) and is perpendicular to y = 5/4x -5?

Apr 20, 2017

$5 y + 4 x = 0$

#### Explanation:

Since the line is perpendicular to another line with slope $\frac{5}{4}$, its slope will be the negative reciprocal of the other line's slope.

Hence the slope of the line is $- \frac{4}{5}$. We also know it passes through $\left(5 , - 4\right)$.

Using

$y = m x + c$

we know

$\text{m (slope) =} - \frac{4}{5}$

therefore

$y = - \frac{4}{5} x + c$

Substituting $\left(5 , - 4\right)$ gives you

$- 4 = - \frac{4}{5} \left(5\right) + c$

$c = 0$

Therefore

$y = - \frac{4}{5} x$

$5 y = - 4 x$

$5 y + 4 x = 0$