# How do you write an equation in point slope form given (–2, 0) and (2, 8)?

Mar 26, 2017

See the entire solution process below:

#### Explanation:

First, we need to determine the slope of the line which goes through the two points given in the problem. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{0}}{\textcolor{red}{2} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{8} - \textcolor{b l u e}{0}}{\textcolor{red}{2} + \textcolor{b l u e}{2}} = \frac{8}{4} = 2$

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope we calculated and the first point from the problem gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{2} \left(x + \textcolor{red}{2}\right)$

We can also substitute the slope we calculated and the second point from the problem giving:

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{2}\right)$