How do you write the equation in point slope form given (5,-8) , (-9,-8)?

Mar 14, 2017

$\left(y + \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{5}\right)$

Or

$\left(y + \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{9}\right)$

Or

$\left(y + \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{a}\right)$ Where $a$ is any value you want.

Explanation:

Because both points have the same $y$ value of $- 8$ we know by definition this is a horizontal line with a slope of $m = 0$.

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 the first point from the problem gives:

$\left(y - \textcolor{red}{- 8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{5}\right)$

$\left(y + \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{5}\right)$

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

$\left(y - \textcolor{red}{- 8}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{- 9}\right)$

$\left(y + \textcolor{red}{8}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{9}\right)$