# How do you write the equation in point slope form given (-6,8) and (4,8)?

Feb 4, 2017

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{6}\right)$

Or

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{4}\right)$

#### Explanation:

First, determine the slope. 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:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{8}}{\textcolor{red}{4} - \textcolor{b l u e}{- 6}}$

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{8}}{\textcolor{red}{4} + \textcolor{b l u e}{6}}$

$m = \frac{0}{10} = 0$

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 and values from the first point gives:

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{- 6}\right)$

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{6}\right)$

We can also substitute the slope and values from the second point giving:

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{4}\right)$