# How do you write the standard form of the equation given (-1,2) and slope 2?

Jan 7, 2018

$2 x - 1 y = - 4$

#### Explanation:

Given the point $\left(\textcolor{red}{\hat{x}} , \textcolor{b l u e}{\hat{y}}\right) = \left(\textcolor{red}{- 1} , \textcolor{b l u e}{2}\right)$ and a slope of $\textcolor{g r e e n}{m} = \textcolor{g r e e n}{2}$

the *slope-point form is:
$y - \textcolor{b l u e}{\hat{y}} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{\hat{x}}\right)$
rarrcolor(white)("xxxx")y-color(blue)(2)=color(green)2(x-color(red)(""(-1)))

We wish to convert this into standard form
$A x + B y = C$ with $A , B , C \in \mathbb{Z} , A \ge 0$

Simplifying our slope-point form
$\textcolor{w h i t e}{\text{XXX}} y - 2 = 2 x + 2$
Exchanging left and right sides
$\textcolor{w h i t e}{\text{XXX}} 2 x + 2 = y - 2$
Subtracting $1 y$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} 2 x - 1 y + 2 = - 2$
Subtracting $2$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} 2 x - 1 y = - 4$
(which is standrd form)