# How do you write an equation of a line with Slope = -2, passing through (0, - 3)?

May 24, 2015

The quick answer is $y = - 2 x - 3$

The equation of a line can be expressed as $y = m x + c$, where $m$ is the slope and $c$ is the intercept - that is the value of $y$ where the line intercepts the $y$ axis.

In your case, the intercept value $c = - 3$, so if we were being particularly pernickity the slope intercept form of the equation would be:

$y = \left(- 2\right) x + \left(- 3\right)$

Another standard form for the equation of a line is called "point slope" form. In general it looks like this:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is some point the line goes through.

In your case, we could write:

$y - \left(- 3\right) = \left(- 2\right) \left(x - 0\right)$

or more simply:

$y + 3 = - 2 x$