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

Jun 18, 2018

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

Explanation:

For a partial variation the value of one variable is:
$\textcolor{w h i t e}{\text{XXX}}$a constant times the value of the other variable
$\textcolor{w h i t e}{\text{XXX}}$plus
$\textcolor{w h i t e}{\text{XXX}}$some constant value.

Any equation that can be written with variables $x$ and $y$, and constants $m$ and $c$, in the form:
$\textcolor{w h i t e}{\text{XXX}} y = m x + c$
is a partial variation

(Some definitions of partial variation add the restriction that $c \ne 0$; that is a partial variation is not also a direct variation).

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

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