How do you write the point slope form of the equation given (-7,7) and (5,-6)?

Mar 20, 2018

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The formula for find the slope of a line is:

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

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ and $\left(\textcolor{red}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$ are two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{7}}{\textcolor{red}{5} - \textcolor{b l u e}{- 7}} = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{7}}{\textcolor{red}{5} + \textcolor{b l u e}{7}} = - \frac{13}{12}$

The point-slope form of a linear equation is: $\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ is a point on the line and $\textcolor{red}{m}$ is the slope.

Substituting the slope we calculated and the values from the first point in the problem gives:

$\left(y - \textcolor{b l u e}{7}\right) = \textcolor{red}{- \frac{13}{12}} \left(x - \textcolor{b l u e}{- 7}\right)$

$\left(y - \textcolor{b l u e}{7}\right) = \textcolor{red}{- \frac{13}{12}} \left(x + \textcolor{b l u e}{7}\right)$

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

$\left(y - \textcolor{b l u e}{- 6}\right) = \textcolor{red}{- \frac{13}{12}} \left(x - \textcolor{b l u e}{5}\right)$

$\left(y + \textcolor{b l u e}{6}\right) = \textcolor{red}{- \frac{13}{12}} \left(x - \textcolor{b l u e}{5}\right)$