# How do you write the equation y+7=1/2(x+2) in standard form?

May 8, 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, I would multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction and to ensure all of the coefficients and constants are integers as require by the Standard Form:

$\textcolor{red}{2} \left(y + 7\right) = \textcolor{red}{2} \cdot \frac{1}{2} \left(x + 2\right)$

$\left(\textcolor{red}{2} \cdot y\right) + \left(\textcolor{red}{2} \cdot 7\right) = \cancel{\textcolor{red}{2}} \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} \left(x + 2\right)$

$2 y + 14 = x + 2$

Next, subtract $\textcolor{red}{14}$ and $\textcolor{b l u e}{x}$ from each side of the equation to place the variables on the left side of the equation and the constant on the right side of the equation:

$- \textcolor{b l u e}{x} + 2 y + 14 - \textcolor{red}{14} = - \textcolor{b l u e}{x} + x + 2 - \textcolor{red}{14}$

$- x + 2 y + 0 = 0 - 12$

$- x + 2 y = - 12$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to ensure the $x$ coefficient is a non-negative integer:

$\textcolor{red}{- 1} \left(- x + 2 y\right) = \textcolor{red}{- 1} \cdot - 12$

$\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{12}$