# How do you write the point slope form of the equation given (1,9) and (-2,-2)?

Apr 11, 2017

See the entire solution process below:

#### Explanation:

First, we must 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:

$m = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{9}}{\textcolor{red}{- 2} - \textcolor{b l u e}{1}} = \frac{- 11}{- 3} = \frac{11}{3}$

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.

We can now substitute the slope we calculated and the values from the first point giving:

$\left(y - \textcolor{red}{9}\right) = \textcolor{b l u e}{\frac{11}{3}} \left(x - \textcolor{red}{1}\right)$

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

$\left(y - \textcolor{red}{- 2}\right) = \textcolor{b l u e}{\frac{11}{3}} \left(x - \textcolor{red}{- 2}\right)$

$\left(y + \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{11}{3}} \left(x + \textcolor{red}{2}\right)$