# How do you write the equation in slope-intercept form of the line that is perpendicular to y=5x+6 but goes through the point (-5,-3)?

Nov 15, 2016

#### Explanation:

Given a line with slope, $m$, any line perpendicular with have a slope $- \frac{1}{m}$.

Therefore, a line that is perpendicular to $y = 5 x + 6$ will have a slope of $m = - \frac{1}{5}$

Start slope intercept form of the equation of a line:

$y = m x + b$

Substitute -5 for x, -3 for y, and $- \frac{1}{5}$ for m:

$- 3 = - \frac{1}{5} \left(- 5\right) + b$

Solve for b:

$b = - 4$

The equation of the line is:

$y = - \frac{1}{5} x - 4$