Question

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

Answer 1

`4x-3y=-2`

Explanation:

The standard form of a linear equation is:
`Ax + By = 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 `4/3x` from both parts:
`y - 4/3x = 4/3x + 2/3 - 4/3x`
`y - 4/3x = 2/3`

By reordering, you get:
`-4/3x + y = 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*(-4/3x + y) = -1*2/3`
`4/3x - y=-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*(4/3x - y)=3*(-2/3)`
`4x-3y=-2`