# How do you write an equation of a line passing through (4,8) and (1,2)?

Jan 31, 2017

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{4}\right)$

Or

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{1}\right)$

#### Explanation:

We can use the point-slope formula to write the equation of a line passing through these two points. First, however, 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 points in the problem gives:

$m = \frac{\textcolor{red}{2} - \textcolor{b l u e}{8}}{\textcolor{red}{1} - \textcolor{b l u e}{4}}$

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

$m = 2$

Now we can use the slope and the first point in the point-slope formula to find an equation.

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.

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{4}\right)$

We can also use the slope and the second point in the point-slope formula to find an equation.

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{1}\right)$