# How do you write an equation in point slope form given S(–10, –3) and T(–1, 1)?

Jul 10, 2017

See a solution process below:

#### Explanation:

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

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

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

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{b l u e}{1} - \textcolor{red}{- 3}}{\textcolor{b l u e}{- 1} - \textcolor{red}{- 10}} = \frac{\textcolor{b l u e}{1} + \textcolor{red}{3}}{\textcolor{b l u e}{- 1} + \textcolor{red}{10}} = \frac{4}{9}$

The point-slope formula is:

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

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

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

$\left(y - \textcolor{red}{- 3}\right) = \textcolor{b l u e}{\frac{4}{9}} \left(x - \textcolor{red}{- 10}\right)$

$\left(y + \textcolor{red}{3}\right) = \textcolor{b l u e}{\frac{4}{9}} \left(x + \textcolor{red}{10}\right)$

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

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{4}{9}} \left(x - \textcolor{red}{- 1}\right)$

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{4}{9}} \left(x + \textcolor{red}{1}\right)$