# How do you write an equation of a line with points (-2,6), (0,0)?

Jan 31, 2017

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{- 3} \left(x + \textcolor{red}{2}\right)$

Or

$y = - 3 x$

#### Explanation:

The point-slope formula can be used to fund and equation for the line having the points given in the problem.

First, 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 problem gives:

$m = \frac{\textcolor{red}{0} - \textcolor{b l u e}{6}}{\textcolor{red}{0} - \textcolor{b l u e}{- 2}}$

$m = \frac{\textcolor{red}{0} - \textcolor{b l u e}{6}}{\textcolor{red}{0} + \textcolor{b l u e}{2}}$

$m = - \frac{6}{2} = - 3$

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.

We can now use the slope we calculated and the first point in the point-slope formula to give:

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{- 3} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{- 3} \left(x + \textcolor{red}{2}\right)$

We can also use the slope we calculated and the second point in the point-slope formula to give:

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

$y = - 3 x$