# How do you write the point slope form of the equation given (0,4) and (1,-4)?

Jan 18, 2017

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{0}\right)$

Or

$\left(y + \textcolor{red}{4}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{1}\right)$

#### Explanation:

First, we need to 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 two points in the problem gives:

$m = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{4}}{\textcolor{red}{1} - \textcolor{b l u e}{0}}$

$m = - \frac{8}{1} = - 8$

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.

Solution 1) Using the calculated slope and the values from the first point in the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{0}\right)$

Solution 1) Using the calculated slope and the values from the second point in the problem gives:

$\left(y - \textcolor{red}{- 4}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{1}\right)$

$\left(y + \textcolor{red}{4}\right) = \textcolor{b l u e}{- 8} \left(x - \textcolor{red}{1}\right)$