# How do you write y - 10 = -2(x - 3)  in standard form?

Jan 25, 2017

$\textcolor{red}{2} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{16}$

#### 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, expand the term in parenthesis on the right side of the equation:

$y - 10 = \left(- 2 \times x\right) + \left(2 \times 3\right)$

$y - 10 = - 2 x + 6$

Next add $\textcolor{red}{2 x}$ and $\textcolor{b l u e}{10}$ to each side of the equation to isolate the $x$ and $y$ term on the left side of the equation and the constants on the other wide of the equation:

$\textcolor{red}{2 x} + y - 10 + \textcolor{b l u e}{10} = \textcolor{red}{2 x} - 2 x + 6 + \textcolor{b l u e}{10}$

$2 x + y - 0 = 0 + 6 + 10$

$2 x + y = 16$