# How do you write y = -1/3x - 9 in standard form?

##### 1 Answer
Mar 1, 2017

$\textcolor{red}{1} x + \textcolor{b l u e}{3} y = \textcolor{g r e e n}{- 27}$

#### 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 this equation to standard form, first, multiply each side of the equation by $\textcolor{red}{3}$ to eliminate the fractions:

$\textcolor{red}{3} \times y = \textcolor{red}{3} \left(- \frac{1}{3} x - 9\right)$

$3 y = \left(\textcolor{red}{3} \times - \frac{1}{3} x\right) - \left(\textcolor{red}{3} \times 9\right)$

$3 y = \left(\cancel{\textcolor{red}{3}} \times - \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x\right) - 27$

$3 y = - 1 x - 27$

Next, add $\textcolor{red}{1 x}$ to each side of the equation to place the $x$ and $y$ variables on the left side of the equation as the standard form requires:

$\textcolor{red}{1 x} + 3 y = \textcolor{red}{1 x} - 1 x - 27$

$1 x + 3 y = 0 - 27$

$\textcolor{red}{1} x + \textcolor{b l u e}{3} y = \textcolor{g r e e n}{- 27}$