How do you write y = 7/2x – 6 in standard form?

Apr 2, 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, multiply both sides of the equation by $\textcolor{red}{2}$ to eliminate the fraction while keeping the equation balanced. The standard form of a linear equation must have coefficients which are integers.

$\textcolor{red}{2} \times y = \textcolor{red}{2} \left(\frac{7}{2} x - 6\right)$

$2 y = \left(\textcolor{red}{2} \times \frac{7}{2} x\right) - \left(\textcolor{red}{2} \times 6\right)$

$2 y = \left(\cancel{\textcolor{red}{2}} \times \frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x\right) - 12$

$2 y = 7 x - 12$

Next, subtract $\textcolor{red}{7 x}$ from each side of the equation to move the $x$ term to the left side of the equation while keeping the equation balanced. The standard form of a linear equation has the $x$ and $y$ terms on the left side of the equation.

$- \textcolor{red}{7 x} + 2 y = - \textcolor{red}{7 x} + 7 x - 12$

$- 7 x + 2 y = 0 - 12$

$- 7 x + 2 y = - 12$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to put the equation in standard form while keeping the equation balanced. In a standard form linear equation the coefficient of the $x$ term should be a positive integer.

$\textcolor{red}{- 1} \left(- 7 x + 2 y\right) = \textcolor{red}{- 1} \times - 12$

$\left(\textcolor{red}{- 1} \times - 7 x\right) + \left(\textcolor{red}{- 1} \times 2 y\right) = 12$

$\textcolor{red}{7} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{12}$