# How do you write the equation of a line in point slope form and slope intercept form given points (-3, -4) (3, -2)?

May 7, 2015

Since both requested forms require the slope, let's start there:

$m = \frac{\Delta y}{\Delta x}$

$= \frac{\left(- 2\right) - \left(- 4\right)}{3 - \left(- 3\right)}$

$= \frac{2}{6} = \frac{1}{3}$

The general point slope form is
$\left(y - y - 1\right) = m \left(x - {x}_{1}\right)$
or, in our example,
$y - \left(- 4\right) = \frac{1}{3} \left(x - \left(- 3\right)\right)$

With a little rearranging we can convert this into the slope intercept form (which in general is $y = m x + b$ with a y-intercept at $b$)

$y + 4 = \frac{1}{3} \left(x + 3\right)$

$y + 4 = \frac{1}{3} x + 1$

$y = \frac{1}{3} x - 3$