# How do you write an equation in standard form given a line that passes through (22,12) with slope 5/6?

Jun 5, 2015

A line passing through $\left(22 , 12\right)$ with slope $\frac{5}{6}$ can be expressed using the point slope form as:
$\textcolor{w h i t e}{\text{XXXX}}$$y - 12 = \frac{5}{6} \left(x - 22\right)$

The standard form for a line is
$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$ where $A \ge 0 , A \epsilon \mathbb{Z}$

So a bit of manipulation of the point slope form is required
$\textcolor{w h i t e}{\text{XXXX}}$$6 \left(y - 12\right) = 5 \left(x - 22\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$6 y - 72 = 5 x - 110$

$\textcolor{w h i t e}{\text{XXXX}}$$- 5 x + 6 y = - 38$

$\textcolor{w h i t e}{\text{XXXX}}$$5 x - 6 y = 38$$\textcolor{w h i t e}{\text{XXXX}}$(standard form)