# How do you write the equation y=1/4x+3 in standard form with integer coefficients?

May 16, 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

To convert to Standard Form for a linear equation, first, subtract $\textcolor{red}{\frac{1}{4} x}$ from each side of the equation to put the $x$ and $y$ variables both on the left side of the equation while keeping the equation balanced:

$- \textcolor{red}{\frac{1}{4} x} + y = - \textcolor{red}{\frac{1}{4} x} + \frac{1}{4} x + 3$

$- \frac{1}{4} x + y = 0 + 3$

$- \frac{1}{4} x + y = 3$

Now, multiply each side of the equation by $\textcolor{red}{- 4}$ to eliminate the fraction and to ensure the $x$ coefficient is positive while keeping the equation balanced:

$\textcolor{red}{- 4} \left(- \frac{1}{4} x + y\right) = \textcolor{red}{- 4} \times 3$

$\left(\textcolor{red}{- 4} \times - \frac{1}{4} x\right) + \left(\textcolor{red}{- 4} \times y\right) = - 12$

$\left(\cancel{\textcolor{red}{- 4}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}}} x\right) - 4 y = - 12$

$\textcolor{red}{1} x - \textcolor{b l u e}{4} y = \textcolor{g r e e n}{- 12}$