# How do you write an equation of a line with slope 2/3 and point is (8, -4)?

Dec 14, 2016

$2 x - 3 y = 28$

#### Explanation:

Given a slope of $\textcolor{g r e e n}{m}$ through a point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$
the slope-point form of the line is
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$

For the given values this becomes
$\textcolor{w h i t e}{\text{XXX")y-color(blue)(} \left(- 4\right)} = \textcolor{g r e e n}{\frac{2}{3}} \left(x - \textcolor{red}{8}\right)$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} 3 y + 12 = 2 x - 16$

or, in standard form
$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y = 28$

or, you might want this in slope-intercept form:
$\textcolor{w h i t e}{\text{XXX}} y = \frac{2}{3} x - \frac{28}{3}$