# How do you write the equation in point slope form given (-1,7) and (8,-2)?

Apr 7, 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:

$m = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{7}}{\textcolor{red}{8} - \textcolor{b l u e}{- 1}} = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{7}}{\textcolor{red}{8} + \textcolor{b l u e}{1}} = - \frac{9}{9} = - 1$

Now, we can write an equation in point-slope form. 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 we calculated and the first point gives:

$\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{- 1}\right)$

Solution 1) $\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{- 1} \left(x + \textcolor{red}{1}\right)$

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

$\left(y - \textcolor{red}{- 2}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{8}\right)$

Solution 2) $\left(y + \textcolor{red}{2}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{8}\right)$