# How do you write the point slope form of the equation given (-8,7) and (-3,-5)?

Jul 6, 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:

$m = \frac{\textcolor{red}{- 5} - \textcolor{b l u e}{7}}{\textcolor{red}{- 3} - \textcolor{b l u e}{- 8}} = \frac{\textcolor{red}{- 5} - \textcolor{b l u e}{7}}{\textcolor{red}{- 3} + \textcolor{b l u e}{8}} = - \frac{12}{5}$

Now, we can used the point-slope formula. 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 now substitute the slope we calculated and the values from the first point in the problem giving:

$\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{- \frac{12}{5}} \left(x - \textcolor{red}{- 8}\right)$

$\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{- \frac{12}{5}} \left(x + \textcolor{red}{8}\right)$

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

$\left(y - \textcolor{red}{- 5}\right) = \textcolor{b l u e}{- \frac{12}{5}} \left(x - \textcolor{red}{- 3}\right)$

$\left(y + \textcolor{red}{5}\right) = \textcolor{b l u e}{- \frac{12}{5}} \left(x + \textcolor{red}{3}\right)$