# How do you write the equation in point slope form given (-3, -2), (2,-1)?

Jan 13, 2017

$\left(y + \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x + \textcolor{red}{3}\right)$

or

$\left(y + \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x - \textcolor{red}{2}\right)$

#### Explanation:

First, we need to 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 our two points gives:

$m = \frac{\textcolor{red}{- 1} - \textcolor{b l u e}{- 2}}{\textcolor{red}{2} - \textcolor{b l u e}{- 3}}$

$m = \frac{\textcolor{red}{- 1} + \textcolor{b l u e}{2}}{\textcolor{red}{2} + \textcolor{b l u e}{3}}$

$m = \frac{1}{5}$

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 values from the two points given in the problem and the slope we calculated results in:

$\left(y - \textcolor{red}{- 2}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x - \textcolor{red}{- 3}\right)$

$\left(y + \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x + \textcolor{red}{3}\right)$

or

$\left(y - \textcolor{red}{- 1}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x - \textcolor{red}{2}\right)$

$\left(y + \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{1}{5}} \left(x - \textcolor{red}{2}\right)$