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

1 Answer

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:
$XXX$ $color(white)("XXX")$ a constant times the value of the other variable
$XXX$ $color(white)("XXX")$ plus
$XXX$ $color(white)("XXX")$ some constant value.

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

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

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

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

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