How do you write the equation y=2x-5 in standard form?

Apr 15, 2017

See the entire 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, we need to move the $x$ term to the left side of the equation by subtracting $\textcolor{red}{2 x}$ from each side of the equation:

$- \textcolor{red}{2 x} + y = - \textcolor{red}{2 x} + 2 x - 5$

$- 2 x + y = 0 - 5$

$- 2 x + y = - 5$

Another requirement is for the $x$ coefficient to be non-negative. Therefore, we must multiply each side of the equation by $\textcolor{red}{- 1}$:

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

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

$2 x - y = 5$

$\textcolor{red}{2} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$