# How do you find a standard form equation for the line y=2/3x-7?

Jul 3, 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, to convert the equation in the problem to standard form we can multiply each side of the equation by $\textcolor{red}{3}$ to eliminate the fractions as required by the formula while keeping the equation balanced:

$\textcolor{red}{3} \cdot y = \textcolor{red}{3} \left(\frac{2}{3} x - 7\right)$

$3 y = \left(\textcolor{red}{3} \cdot \frac{2}{3} x\right) - \left(\textcolor{red}{3} \cdot 7\right)$

$3 y = \left(\cancel{\textcolor{red}{3}} \cdot \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x\right) - 21$

$3 y = 2 x - 21$

Next, we can subtract $\textcolor{red}{2 x}$ from each side of the equation to isolate the $x$ and $y$ term on the left side of the equation as required by the formula while keeping the equation balanced:

$- \textcolor{red}{2 x} + 3 y = - \textcolor{red}{2 x} + 2 x - 21$

$- 2 x + 3 y = 0 - 21$

$- 2 x + 3 y = - 21$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to convert the $x$ coefficient to a positive integer as required in the formula while keeping the equation balanced:

$\textcolor{red}{- 1} \left(- 2 x + 3 y\right) = \textcolor{red}{- 1} \cdot - 21$

$\left(\textcolor{red}{- 1} \cdot - 2 x\right) + \left(\textcolor{red}{- 1} \cdot 3 y\right) = 21$

$\textcolor{red}{2} x - \textcolor{b l u e}{3} y = \textcolor{g r e e n}{21}$