# How do you write y-10=2(x-8) in standard form?

Oct 17, 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

First, we can expand the terms on the right side of the equation:

$y - 10 = \textcolor{red}{2} \left(x - 8\right)$

$y - 10 = \left(\textcolor{red}{2} \times x\right) - \left(\textcolor{red}{2} \times 8\right)$

$y - 10 = 2 x - 16$

Next, we can add $\textcolor{red}{10}$ and subtract $\textcolor{b l u e}{2 x}$ from each side of the equation:

$- \textcolor{b l u e}{2 x} + y - 10 + \textcolor{red}{10} = - \textcolor{b l u e}{2 x} + 2 x - 16 + \textcolor{red}{10}$

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

$- 2 x + y = - 6$

Now, multiply each side of the equation by $\textcolor{\mathmr{and} a n \ge}{- 1}$

$\textcolor{\mathmr{and} a n \ge}{- 1} \left(- 2 x + y\right) = \textcolor{\mathmr{and} a n \ge}{- 1} \times - 6$

$\left(\textcolor{\mathmr{and} a n \ge}{- 1} \times - 2 x\right) + \left(\textcolor{\mathmr{and} a n \ge}{- 1} \times y\right) = 6$

$\textcolor{red}{2} x + \left(- \textcolor{b l u e}{y}\right) = \textcolor{g r e e n}{6}$

or

$\textcolor{red}{2} x - \textcolor{b l u e}{y} = \textcolor{g r e e n}{6}$