Answer
$x - 3y = 6$
Work Step by Step
To rewrite an equation in standard form, we use the following formula:
$Ax + By = C$
For the equation $y + 4 = \frac{1}{3}(x + 6)$, we first distribute the terms:
$y + 4 = \frac{1}{3}x + \frac{1}{3}(6)$
Multiply to simplify:
$y + 4 = \frac{1}{3}x + \frac{6}{3}$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $3$:
$y + 4 = \frac{1}{3}x + 2$
Subtract $4$ from each side of the equation to isolate constants on one side of the equation:
$y = \frac{1}{3}x + 2 - 4$
Subtract to simplify:
$y = \frac{1}{3}x - 2$
Move the $x$ term to the other side of the equation by subtracting $\frac{1}{3}x$ from both sides of the equation:
$-\frac{1}{3}x + y = -2$
Divide both sides by $-1$ to make the $x$ term positive:
$\frac{1}{3}x - y = 2$
To make all values integers, we multiply everything by the denominator of the fraction, which will make the fraction an integer:
$3(\frac{1}{3}x - y) = 3(2)$
Distribute terms first, according to order of operations:
$\frac{3}{3}x - 3y = 6$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $3$:
$x - 3y = 6$
