# How do you write the equation of a line in point slope form and slope intercept form given points (3, -8) (-2, 5)?

May 27, 2015

Given the points $\left(3 , - 8\right)$ and $\left(- 2 , 5\right)$
both the point-slope form and the slope-intercept form require that we first determine the slope.

The slope can be calculated as
$m = \frac{\Delta y}{\Delta x} = \frac{5 - \left(- 8\right)}{- 2 - 3} = - \frac{13}{5}$

Using the slope $m = - \frac{13}{5}$ and the point $\left(3 , - 8\right)$
the slope-point form ($y - {y}_{1} = m \left(x - {x}_{1}\right)$) is

$y - \left(- 8\right) = - \frac{13}{5} \left(x - 3\right)$
or
$y + 8 = - \frac{13}{5} \left(x - 3\right)$

The slope-point form can be converted into the slope-intercept form ($y = m x + b$) by some minor re-arranging of terms:
$y + 8 = - \frac{13}{5} \left(x - 3\right)$

$\rightarrow y = - \frac{13}{5} x + \frac{39}{5} - 8$

$\rightarrow y = - \frac{13}{5} x - \frac{1}{8}$