# Given (2,-2), and and y intercept 4, how do you find the equation of the line?

Jan 7, 2017

Use the point-slope - see full explanation below:

#### Explanation:

We have been given two points (the y-intercept is point $\left(0 , 4\right)$) so we can use the point-slope formula to find the equation for the line.

First, we must find the slope which requires two points:

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 our two points gives:

$m = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{4}}{\textcolor{red}{2} - \textcolor{b l u e}{0}}$

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

$m = - 3$

Now, having the slope, we can use it and one of the points to use the point-slope formula to find the equation of the line:

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 our slope and one of the points gives:

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

We can also put it into the more familiar slope-intercept form by solving for $y$:

$y - \textcolor{red}{4} = \textcolor{b l u e}{- 3} x$

$y - \textcolor{red}{4} + 4 = \textcolor{b l u e}{- 3} x + 4$

$y - 0 = \textcolor{b l u e}{- 3} x + 4$

$y = \textcolor{b l u e}{- 3} x + 4$