# How do you write the equation in point slope form given (2,3) and (4,-6)?

Jan 31, 2017

$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{- \frac{9}{2}} \left(x - \textcolor{red}{2}\right)$

Or

$\left(y + \textcolor{red}{6}\right) = \textcolor{b l u e}{- \frac{9}{2}} \left(x - \textcolor{red}{4}\right)$

#### Explanation:

First, we must find 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 two points in the problem gives:

$m = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{3}}{\textcolor{red}{4} - \textcolor{b l u e}{2}}$

$m = - \frac{9}{2}$

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.

Now we can use the slope we calculated and the first point to give:

$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{- \frac{9}{2}} \left(x - \textcolor{red}{2}\right)$

We can also use the slope we calculated and the second point to give:

$\left(y - \textcolor{red}{- 6}\right) = \textcolor{b l u e}{- \frac{9}{2}} \left(x - \textcolor{red}{4}\right)$

$\left(y + \textcolor{red}{6}\right) = \textcolor{b l u e}{- \frac{9}{2}} \left(x - \textcolor{red}{4}\right)$