# How do you find the equation of a line that Contains point (5, -3) and is perpendicular to y=5x?

Jan 18, 2016

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

#### Explanation:

For finding an equation of a perpendicular line, we start with finding the slope of the given line. Slope of the perpendicular line is negative reciprocal of the given slope. For example, if the slope is $m$ then the slope of the perpendicular would be $- \frac{1}{m}$

Equation of the form $y = m x + b$ has the slope as $m$

Using this knowledge, we can see that the slope of the line $y = 5 x$ is $5$

The slope of the perpendicular line is $- \frac{1}{5}$

We can say our line would be

$y = - \frac{1}{5} x + b$

We need to find $b$ to find the equation. This is where the point$\left(5 , - 3\right)$ is used.

Let us substitute the value $x = 5$ and $y = - 3$ in the equation $y = - \frac{1}{5} x + b$

We get,
$- 3 = - \frac{1}{5} \left(5\right) + b$
$- 3 = - 1 + b$
Add $1$ to both the sides.

$- 3 + 1 = b$

$- 2 = b$

Our equation becomes $y = - \frac{1}{5} x - 2$