# What is the slope of the line passing through  (-4,-8); (-3,-3)?

Jun 7, 2018

$\left(y + 8\right) = 5 \left(x + 4\right)$

#### Explanation:

First you determine the slope:

$\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right) = \left(- 4 , - 8\right)$

$\left(\textcolor{red}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right) = \left(- 3 , - 3\right)$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{\left(- 8\right)}}{\textcolor{red}{- 3} - \textcolor{b l u e}{\left(- 4\right)}}$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{- 3} + \textcolor{b l u e}{8}}{\textcolor{red}{- 3} + \textcolor{b l u e}{4}} = \frac{5}{1} = 5$

Now use the Point Slope form of a line:

$\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$\left(y - \textcolor{b l u e}{\left(- 8\right)}\right) = \textcolor{g r e e n}{5} \left(x - \textcolor{b l u e}{\left(- 4\right)}\right)$

$\left(y + \textcolor{b l u e}{8}\right) = \textcolor{g r e e n}{5} \left(x + \textcolor{b l u e}{4}\right)$

graph{(y+8) = 5(x+4) [-21.96, 18.04, -3.16, 16.84]}