# How do you write the equation y=3x-5 in standard form and identify A, B, C?

Jul 24, 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, subtract $\textcolor{red}{3 x}$ from each side of the equation so both the $x$ and $y$ terms are on the left side of the equation as required by the Standard form while keeping the equation balanced.

$- \textcolor{red}{3 x} + y = - \textcolor{red}{3 x} + 3 x - 5$

$- 3 x + y = 0 - 5$

$- 3 x + y = - 5$

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

$\textcolor{red}{- 1} \left(- 3 x + y\right) = \textcolor{red}{- 1} \cdot - 5$

$\left(\textcolor{red}{- 1} \cdot - 3 x\right) + \left(\textcolor{red}{- 1} \cdot y\right) = 5$

$\textcolor{red}{3} x + \textcolor{b l u e}{- 1} y = \textcolor{g r e e n}{5}$

Or

$\textcolor{red}{3} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$

$\textcolor{red}{A = 3}$

$\textcolor{b l u e}{B = - 1}$

$\textcolor{g r e e n}{C = 5}$