# How do you write y=x/3-6 in standard form?

Jan 13, 2017

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

The first step is to multiple each side of the equation by $\textcolor{red}{3}$ to obtain all integers:

$\textcolor{red}{3} \times y = \textcolor{red}{3} \times \left(\frac{x}{3} - 6\right)$

$3 y = \left(\textcolor{red}{3} \times \frac{x}{3}\right) - \left(\textcolor{red}{3} \times 6\right)$

$3 y = \left(\cancel{\textcolor{red}{3}} \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right) - 18$

$3 y = x - 18$

Next step is to move $x$ to the left side of the equation by subtracting $\textcolor{red}{x}$ from each side of the equation:

$- x + 3 y = 0 - 18$

$- x + 3 y = - 18$

Now we can multiply each side of the equation by $\textcolor{red}{- 1}$ to make the coefficient of $x$ positive. The coefficient is $- 1$ currently.

$\textcolor{red}{- 1} \times \left(- x + 3 y\right) = \textcolor{red}{- 1} \times - 18$

$x - 3 y = 18$

or

$\textcolor{red}{1} x - \textcolor{b l u e}{3} y = \textcolor{g r e e n}{18}$