# How do you write the point-slope form of an equation of the line that passes through the given point (-2,5), (9,5)?

Aug 4, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line. 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:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{5}}{\textcolor{red}{9} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{5} - \textcolor{b l u e}{5}}{\textcolor{red}{9} + \textcolor{b l u e}{2}} = \frac{0}{11} = 0$

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 $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

We can substitute the slope we calculated and the values from the first point in the problem line to give the formal point-slope form for the equation of the line represented by the two points in the problem.

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{0} \left(x + \textcolor{red}{2}\right)$

We can also substitute the slope we calculated and the values from the second point in the problem line to give the formal point-slope form for the equation of the line represented by the two points in the problem.

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{9}\right)$

If necessary, we can also reduce both these equations down to:

$y - \textcolor{red}{5} = \textcolor{b l u e}{0}$

Or

$y = 5$