# How do you write the equation given (-3,-3); (0,0)?

Jan 26, 2017

$\left(y + \textcolor{red}{3}\right) = \textcolor{b l u e}{1} \left(x + \textcolor{red}{3}\right)$

Or

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{0}\right)$

Or

$y = x$

#### Explanation:

To write an equation for the line going through these two points we can use the point slope formula.

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 two points gives:

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

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

$m = \frac{3}{3} = 1$

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 gives:

$\left(y - \textcolor{red}{- 3}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{- 3}\right)$

$\left(y + \textcolor{red}{3}\right) = \textcolor{b l u e}{1} \left(x + \textcolor{red}{3}\right)$

Substituting the slope we calculate and the second point gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{1} \left(x - \textcolor{red}{0}\right)$

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

$y = x$