# How do you write an equation of a line with Slope = –5, passing through (–4, –2)?

May 24, 2015

There are a couple of standard forms of equation of a line:

(1) Point slope form: $y - {y}_{0} = m \left(x - {x}_{0}\right)$, where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is a point on the line.

So we can write the equation of our line as:

$y - \left(- 2\right) = - 5 \left(x - \left(- 4\right)\right)$

that is:

$y + 2 = - 5 \left(x + 4\right)$

(2) Slope intercept form: $y = m x + c$, where $m$ is the slope and $c$ is the intercept - i.e. the $y$ coordinate of the intersection of the line with the $y$ axis.

Subtracting $m x$ from both sides of this line equation, we find that $c = y - m x$.

In our case, substituting our example point $\left(- 4 , - 2\right)$ and slope $m = - 5$, we find:

$c = - 2 - \left(- 5\right) \left(- 4\right) = - 2 - 20 = - 22$

So we can write the equation of our line as:

$y = \left(- 5\right) x + \left(- 22\right)$

that is:

$y = - 5 x - 22$