Question

What variation is y=x+2? and also 2x-y=1?

Answer 1

Both equations are partial variations
Neither is a direct nor an inverse variation.

Explanation:

For a partial variation the value of one variable is:
`color(white)("XXX")`a constant times the value of the other variable
`color(white)("XXX")`plus
`color(white)("XXX")`some constant value.

Any equation that can be written with variables `x` and `y`, and constants `m` and `c`, in the form:
`color(white)("XXX")y=mx+c`
is a partial variation

(Some definitions of partial variation add the restriction that `c!=0`; that is a partial variation is not also a direct variation).

`y=x+2` is an obvious partial variation (with `m=1` and `c=2`).

`2x-y=1` can be written as `y=2x+1` and is therefore also a partial variation (with `m=2` and `c=1`).