# How do you write  y = 4 x – 7 in standard form?

Aug 6, 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 $\textcolor{red}{4 x}$ from each side of the equation to place both the $x$ and $y$ variables on the left side of the equation as required by the formula:

$- \textcolor{red}{4 x} + y = - \textcolor{red}{4 x} + 4 x - 7$

$- 4 x + y = 0 - 7$

$- 4 x + y = - 7$

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

$\textcolor{red}{- 1} \left(- 4 x + y\right) = \textcolor{red}{- 1} \times - 7$

$\left(\textcolor{red}{- 1} \times - 4 x\right) + \left(\textcolor{red}{- 1} \times y\right) = 7$

$\textcolor{red}{4} x + \textcolor{b l u e}{- 1} y = \textcolor{g r e e n}{7}$

Or

$\textcolor{red}{4} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{7}$

Or

$\textcolor{red}{4} x - y = \textcolor{g r e e n}{7}$