# How do you write y = 3 x + 1 in standard form?

Mar 30, 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 transform the equation in the problem to standard form, first, subtract $\textcolor{red}{3 x}$ from each side of the equation to move the $x$ term to the left side of the equation while keeping the equation balanced:

$- \textcolor{red}{3 x} + y = - \textcolor{red}{3 x} + 3 x + 1$

$- 3 x + y = 0 + 1$

$- 3 x + y = 1$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to make the coefficient of the $x$ term positive:

$\textcolor{red}{- 1} \left(- 3 x + y\right) = \textcolor{red}{- 1} \times 1$

$\left(\textcolor{red}{- 1} \times - 3 x\right) + \left(\textcolor{red}{- 1} \times y\right) = - 1$

$\textcolor{red}{3} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{- 1}$