# What is the equation in point-slope form and slope intercept form for the line given (-6,-4) AND (2,-5)?

Jun 18, 2018

$y + 4 = \left(- \frac{1}{8}\right) \left(x + 6\right)$

#### Explanation:

For the given points $\left({x}_{1} , {y}_{1}\right) = \left(- 6 , - 4\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(2 , - 5\right)$

the slope can be determined as $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 5 - \left(- 4\right)}{2 - \left(- 6\right)} = - \frac{1}{8}$

Using a general variable point $\left(x , y\right)$ and $\left({x}_{1} , {y}_{1}\right)$ (as above)
we have the slope $m = \frac{y - \left(- 4\right)}{x - \left(- 6\right)} = \frac{y + 4}{x + 6}$

Since the slope is constant for all points on a straight line
$\textcolor{w h i t e}{\text{XXX}} \frac{y + 4}{x + 6} = - \frac{1}{8}$

$\Rightarrow y + 4 = \left(- \frac{1}{8}\right) \left(x + 6\right)$

Which is the slope-point form with
$\textcolor{w h i t e}{\text{XXX}}$slope $= \left(- \frac{1}{8}\right)$
and
$\textcolor{w h i t e}{\text{XXX}}$ the point: $\left(- 6 , - 4\right)$