# How do you write an equation of a line that has a intercept of 2 and passes through (12, 4)?

Oct 25, 2016

$\textcolor{g r e e n}{x - 6 y = - 12}$

#### Explanation:

If the line has a y-intercept of $2$ then it passes through $\left({x}_{1} , {y}_{1}\right) = \left(0 , 2\right)$
and since we are told that it also passes through $\left({x}_{2} , {y}_{2}\right) = \left(12 , 4\right)$
we can write the line's equation in two-point form as:
$\textcolor{w h i t e}{\text{XXX}} \frac{y - 2}{x - 0} = \frac{4 - 2}{12 - 0}$

Simplifying:
$\textcolor{w h i t e}{\text{XXX}} y - 2 = x \left(\frac{1}{6}\right)$

$\textcolor{w h i t e}{\text{XXX}} 6 y - 12 = x$

or in standard form:
$\textcolor{w h i t e}{\text{XXX}} x - 6 y = - 12$