How do you write y = 1/2x-1 in standard form?

Jul 19, 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 eliminate the fraction and ensure all of the coefficients are integers as required by the formula while keeping the equation balanced:

$\textcolor{red}{2} \cdot y = \textcolor{red}{2} \left(\frac{1}{2} x - 1\right)$

$2 y = \left(\textcolor{red}{2} \cdot \frac{1}{2} x\right) - \left(\textcolor{red}{2} \cdot 1\right)$

$2 y = \frac{2}{2} x - 2$

$2 y = 1 x - 2$

Next, subtract $\textcolor{red}{1 x}$ from each side of the equation so the $x$ and $y$ terms are on the left side of the equation while keeping the equation balanced:

$- \textcolor{red}{1 x} + 2 y = - \textcolor{red}{1 x} + 1 x - 2$

$- 1 x + 2 y = 0 - 2$

$- 1 x + 2 y = - 2$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to make the $x$ coefficient non-negative as required by the formula while keeping the equation balanced:

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

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

$\textcolor{red}{1} x + \textcolor{b l u e}{- 2} y = \textcolor{g r e e n}{2}$

$\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{2}$