# How do you write  y - 4 = 2.5(x + 3) in standard form?

Jul 8, 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, multiply each side of the equation by $\textcolor{red}{2}$ to ensure all coefficients are integers:

$\textcolor{red}{2} \left(y - 4\right) = \textcolor{red}{2} \times 2.5 \left(x + 3\right)$

$2 y - 8 = 5 \left(x + 3\right)$

Next, expand the terms on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$2 y - 8 = \textcolor{red}{5} \left(x + 3\right)$

$2 y - 8 = \left(\textcolor{red}{5} \times x\right) + \left(\textcolor{red}{5} \times 3\right)$

$2 y - 8 = 5 x + 15$

Then, add $\textcolor{red}{8}$ and subtract $\textcolor{b l u e}{5 x}$ from each side of the equation to place the $x$ and $y$ terms on the left side of the equation and constant on the right side of the equation while keeping the equation balanced:

$- \textcolor{b l u e}{5 x} + 2 y - 8 + \textcolor{red}{8} = - \textcolor{b l u e}{5 x} + 5 x + 15 + \textcolor{red}{8}$

$- 5 x + 2 y - 0 = 0 + 23$

$- 5 x + 2 y = 23$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to ensure the $x$ coefficient is positive while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 5 x + 2 y\right) = \textcolor{red}{- 1} \times 23$

$\left(\textcolor{red}{- 1} \times - 5 x\right) + \left(\textcolor{red}{- 1} \times 2 y\right) = - 23$

$\textcolor{red}{5} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{- 23}$