How do you write the equation in point slope form given (0,0) and (-4,3)?

Feb 15, 2017

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

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- \frac{3}{4}} \left(x - \textcolor{red}{0}\right)$

Explanation:

First, we need to determine the slope of the line. 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:

$m = \frac{\textcolor{red}{3} - \textcolor{b l u e}{0}}{\textcolor{red}{- 4} - \textcolor{b l u e}{0}} = - \frac{3}{4}$

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 calculated and the second point gives:

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

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

We can also substitute the slope we calculated and the first point giving:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- \frac{3}{4}} \left(x - \textcolor{red}{0}\right)$