# How do you write  y - 3 = -2.4(x - 5)  in standard form?

Feb 15, 2017

$\textcolor{red}{12} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{75}$

#### 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 terms in parenthesis:

$y - 3 = \left(- 2.4 \times x\right) + \left(2.4 \times 5\right)$

$y - 3 = - 2.4 x + 12$

Next, add $\textcolor{red}{3}$ and $\textcolor{b l u e}{2.4 x}$ to each side of the equation to move towards the standard form while keeping the equation balanced:

$\textcolor{b l u e}{2.4 x} + y - 3 + \textcolor{red}{3} = \textcolor{b l u e}{2.4 x} - 2.4 x + 12 + \textcolor{red}{3}$

$2.4 x + y - 0 = 0 + 15$

$2.4 x + y = 15$

Now, we multiply each side of the equation by $\textcolor{red}{5}$ to convert all coefficients to integers while keeping the equation balanced:

$\textcolor{red}{5} \left(2.4 x + y\right) = \textcolor{red}{5} \times 15$

$\left(\textcolor{red}{5} \times 2.4 x\right) + \left(\textcolor{red}{5} \times y\right) = 75$

$\textcolor{red}{12} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{75}$