# How do you write an equation in point slope form that passes through (0, -4) with slope -7?

May 26, 2015

In point slope form, the equation of the line is

$y - \left(- 4\right) = - 7 \left(x - 0\right)$

This is of the 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 through which the line passes.

If we are less strict about it, this is written more cleanly as:

$y + 4 = - 7 x$

May 26, 2015

Given a point $\left({x}_{1} , {y}_{1}\right)$ and a slope of $m$
the point-slope form of its linear equation is
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Given the point $\left({x}_{1} , {y}_{1}\right) = \left(0 , - 4\right)$ and the slope $m = \left(- 7\right)$
this becomes
$y - \left(- 4\right) = \left(- 7\right) \left(x - 0\right)$

This, of course, could be simplified; perhaps as
$y + 4 = - 7 x$
but this loses some of the explicit information in the original form.