# How do you write y + 1 = x + 2 in standard form?

May 14, 2017

See a solution process below:

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

First, subtract $\textcolor{red}{1}$ and $\textcolor{b l u e}{x}$ from each side of the equation to have the $x$ and $y$ term on the left side of the equation and the constant on the right side as required by the Standard Form for a linear equation while keeping the equation balanced:

$- \textcolor{b l u e}{x} + y + 1 - \textcolor{red}{1} = - \textcolor{b l u e}{x} + x + 2 - \textcolor{red}{1}$

$- x + y + 0 = 0 + 1$

$- x + y = 1$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to transform the coefficient of the $x$ variable to a positive integer as required by the Standard Form for a linear equation while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- x + y\right) = \textcolor{red}{- 1} \cdot 1$

$\left(\textcolor{red}{- 1} \cdot - x\right) + \left(\textcolor{red}{- 1} \cdot y\right) = - 1$

$1 x + \left(- 1 y\right) = - 1$

$\textcolor{red}{1} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{- 1}$