# How do you write the equation in point slope form given (4,0) and (0,5)?

Mar 6, 2017

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- \frac{5}{4}} \left(x - \textcolor{red}{4}\right)$

Or

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- \frac{5}{4}} \left(x - \textcolor{red}{0}\right)$

#### 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:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{4}} = \frac{5}{-} 4 = - \frac{5}{4}$

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 calculate and the first point from the problem gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- \frac{5}{4}} \left(x - \textcolor{red}{4}\right)$

We can also substitute the slope we calculate and the second point from the problem giving:

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- \frac{5}{4}} \left(x - \textcolor{red}{0}\right)$