# How do you write the equation y=2/3x+1 in standard form and identify A, B, C?

Sep 9, 2017

$2 x - 3 y = - 3$

#### Explanation:

$\text{the equation of a line in "color(blue)"standard form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where A is a positive integer and B, C are integers.

$\text{rearrange "y=2/3x+1" into this form}$

$\text{multiply through by 3 to eliminate the fraction}$

$\Rightarrow 3 y = 2 x + 3$

$\text{subtract 3y from both sides}$

$\cancel{3 y} \cancel{- 3 y} = 2 x - 3 y + 3$

$\Rightarrow 0 = 2 x - 3 y + 3$

$\text{subtract 3 from both sides}$

$0 - 3 = 2 x - 3 y \cancel{+ 3} \cancel{- 3}$

$\Rightarrow 2 x - 3 y = - 3 \leftarrow \textcolor{red}{\text{ in standard form}}$

$\Rightarrow A = 2 , B = - 3 \text{ and } C = - 3$