# How do you write the point slope form of the equation given (3,-3) and (5,0)?

Jul 17, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line represented by the two points in the problem. 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:

$m = \frac{\textcolor{red}{0} - \textcolor{b l u e}{- 3}}{\textcolor{red}{5} - \textcolor{b l u e}{3}} = \frac{\textcolor{red}{0} + \textcolor{b l u e}{3}}{\textcolor{red}{5} - \textcolor{b l u e}{3}} = \frac{3}{2}$

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.

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

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

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

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

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{3}{2}} \left(x - \textcolor{red}{5}\right)$

Or

$y = \textcolor{b l u e}{\frac{3}{2}} \left(x - \textcolor{red}{5}\right)$