# How do you write y = 1/4x - 5 in standard form?

Jan 13, 2017

#### 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

The first step is to eliminate all fractions by multiplying both sides of the equation by $\textcolor{red}{4}$:

$\textcolor{red}{4} \times y = \textcolor{red}{4} \times \left(\frac{1}{4} x - 5\right)$

$4 y = \left(\textcolor{red}{4} \times \frac{1}{4} x\right) - \left(\textcolor{red}{4} \times 5\right)$

$4 y = \left(\cancel{\textcolor{red}{4}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} x\right) - 20$

$4 y = 1 x - 20$

Next step is to move the $x$ term to the left side of the equation by subtracting $\textcolor{red}{1 x}$ from each side of the equation:

$- \textcolor{red}{1 x} + 4 y = - \textcolor{red}{1 x} + 1 x - 20$

$- 1 x + 4 y = - 0 - 20$

$- 1 x + 4 y = - 20$

Now, to make the coefficient of $x$ positive we need to multiply both sides of the equation by $\textcolor{red}{- 1}$

$\textcolor{red}{- 1} \times \left(- 1 x + 4 y\right) = \textcolor{red}{- 1} \times - 20$

(color(red)(-1) xx -1x) + ((color(red)(-1) xx 4y) = 20

$1 x - 4 y = 20$

or

$\textcolor{red}{1} x - \textcolor{b l u e}{4} y = \textcolor{g r e e n}{20}$