# How do you write y=4/3x+2/3 in standard form?

Jun 28, 2015

$4 x - 3 y = - 2$

#### Explanation:

The standard form of a linear equation is:
$A x + B y = C$
$A$ can not be negative. $A$, $B$ and $C$ should all be integers.

The first thing we should do is move the $x$ over to the left part of the equation. You can do this by substracting $\frac{4}{3} x$ from both parts:
$y - \frac{4}{3} x = \frac{4}{3} x + \frac{2}{3} - \frac{4}{3} x$
$y - \frac{4}{3} x = \frac{2}{3}$

By reordering, you get:
$- \frac{4}{3} x + y = \frac{2}{3}$

Now we need to make sure that the number that's before the $x$ ($A$) is positive. You can do this by multiplying both parts by $- 1$:

$- 1 \cdot \left(- \frac{4}{3} x + y\right) = - 1 \cdot \frac{2}{3}$
$\frac{4}{3} x - y = - \frac{2}{3}$

Now, all we need to do is make A, B and C integers. You can always do this by multiplying by the LCM of all the denominators ($3$, $1$ and $3$). This LCM is $3$:

$3 \cdot \left(\frac{4}{3} x - y\right) = 3 \cdot \left(- \frac{2}{3}\right)$
$4 x - 3 y = - 2$