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

Aug 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, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by a negative $1$:

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

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

$y - 4 = - x + 1$

Now, add $\textcolor{red}{4}$ and $\textcolor{b l u e}{x}$ to each side of the equation to ensure both the $x$ and $y$ variables are on the left side of the equation and the constants are on the right side of the equation:

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

$x + y - 0 = 0 + 5$

$x + y = 5$

Or

$\textcolor{red}{1} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$