Question

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

Answer 1

`x-y=-3`

Explanation:

The standard form of a linear equation is `Ax+By=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 = \cancelcolor(blue)(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:
`\color(green)(-1)*(y-x)=\color(green)(-1)*3`
`-y+x=-3`
After some reordering you get:
`x-y=-3`