# How do you write an equation that contains points (5, -3) and is perpendicular to y=5x?

Mar 13, 2018

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

#### Explanation:

We know that this point goes through a point, but in order to define a line we need either two points or a point and a slope.

We can get that slope from the above equation. We know that the new line will have slope perpendicular to five. Perpendicularity means negative inverse, i.e. $m = - \frac{1}{5}$.

From that, we know point-slope form:
$y - {y}_{1} = m \left(x - {x}_{1}\right) \implies y + 3 = - \frac{1}{5} \left(x - 5\right)$
$y = - \frac{1}{5} x - 2$