# How do you write y - 2 = - 1/2 (x - 4)  in standard form?

Mar 16, 2017

See the entire 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

To start, multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction and keep the equation balanced:

$\textcolor{red}{2} \left(y - 2\right) = \textcolor{red}{2} \times - \frac{1}{2} \left(x - 4\right)$

$\left(\textcolor{red}{2} \times y\right) - \left(\textcolor{red}{2} \times 2\right) = - \frac{\textcolor{red}{2}}{2} \left(x - 4\right)$

$2 y - 4 = - 1 \left(x - 4\right)$

$2 y - 4 = \left(- 1 \times x\right) - \left(- 1 \times 4\right)$

$2 y - 4 = - 1 x - \left(- 4\right)$

$2 y - 4 = - 1 x + 4$

Now, add $\textcolor{b l u e}{4}$ and $\textcolor{red}{1 x}$ to each side of the equation to put the $x$ and $y$ terms on the left side of the equation and the constant on the right side of the equation while keeping the equation balanced:

$\textcolor{red}{1 x} + 2 y - 4 + \textcolor{b l u e}{4} = \textcolor{red}{1 x} - 1 x + 4 + \textcolor{b l u e}{4}$

$\textcolor{red}{1 x} + 2 y - 0 = 0 + 8$

$\textcolor{red}{1} x + \textcolor{b l u e}{2} y = \textcolor{g r e e n}{8}$