# How do you convert y=2x-3 in to standard form?

May 19, 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

Because both of the coefficients and the constant are integers we can first subtract $\textcolor{red}{2 x}$ from each side of the equation to group the $x$ and $y$ variable on the left side of the equation while keeping the equation balanced:

$- \textcolor{red}{2 x} + y = - \textcolor{red}{2 x} + 2 x - 3$

$- 2 x + y = 0 - 3$

$- 2 x + y = - 3$

Now, we multiply each side of the equation by $\textcolor{red}{- 1}$ to convert the $x$ coefficient to a positive coefficient while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 2 x + y\right) = \textcolor{red}{- 1} \times - 3$

$\left(\textcolor{red}{- 1} \times - 2 x\right) + \left(\textcolor{red}{- 1} \times y\right) = 3$

$\textcolor{red}{2} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{3}$