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

Jul 3, 2015

$x - y = - 3$

#### Explanation:

The standard form of a linear equation is $A x + B y = C$
It is most of the time also stated that $A$ must be positive and $A$, $B$ and $C$ should all be integers.

$y = x + 3$
You can subtract $x$ from both sides, so you get:
$y - x = \setminus \cancel{\textcolor{b l u e}{x - x}} + 3$
$y - x = 3$
This is sometimes regarded as the standard form, but most of the time, you need to make sure that $A$ is positive, and it is currently $- 1$. How can we change a negative number to a positive number: we multiply by $- 1$. Also, whatever you do at the left part, you must also do at the right part:
$\setminus \textcolor{g r e e n}{- 1} \cdot \left(y - x\right) = \setminus \textcolor{g r e e n}{- 1} \cdot 3$
$- y + x = - 3$
After some reordering you get:
$x - y = - 3$