# How do you write y + 3 = 3(x - 2) in standard form?

Feb 7, 2017

$\textcolor{red}{3} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{9}$

#### 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

We can transform to this form as follows:

$y + 3 = \left(3 \times x\right) - \left(3 \times 2\right)$

$y + 3 = 3 x - 6$

$y + 3 - \textcolor{red}{3} - \textcolor{b l u e}{3 x} = 3 x - 6 - \textcolor{red}{3} - \textcolor{b l u e}{3 x}$

$- \textcolor{b l u e}{3 x} + y + 3 - \textcolor{red}{3} = 3 x - \textcolor{b l u e}{3 x} - 6 - \textcolor{red}{3}$

$- 3 x + y + 0 = 0 - 9$

$- 3 x + y = - 9$

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

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

$\textcolor{red}{3} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{9}$