# How do you write the equation of the line in the form AX+BY=C if (2,5) ; m=3/1?

Sep 16, 2015

#3x-1y=1

#### Explanation:

Given the point $\left(2 , 5\right)$ and the slope $m = \frac{3}{1}$
we can start with the slope-point form for the line:
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
or, for the given values:
$\textcolor{w h i t e}{\text{XXX}} \left(y - 5\right) = 3 \left(x - 2\right)$

Simplifying
$\textcolor{w h i t e}{\text{XXX}} y - 5 = 3 x - 6$

Rearranging so variables are on the left and constant is on the right:
$\textcolor{w h i t e}{\text{XXX}} - 3 x + y = - 1$

There is normally a requirement that $A$ of $A x + B y = C$ be $\ge 0$
In this case:
$\textcolor{w h i t e}{\text{XXX}} 3 x - 1 y = 1$