Concept

Direct Variation

When the quotient of two variables is equal to a constant, they are said to have direct variation, or direct proportionality. Algebraically, this relationship is represented as the constant $k$ being equal to the ratio of $y$ to $x .$

$k = \frac{y}{x} \Leftrightarrow y = k x$

This relationship can also be described graphically by a linear function that passes through the origin.

Concept

Inverse Variation

Two quantities are said to have inverse variation when the product of $x$ and $y$ is constant.

$k = x y \Leftrightarrow y = \frac{k}{x}$

Concept

Joint Variation

A joint variation, also known as joint proportionality, occurs when one variable depends on two or more variables and varies directly with each of them when the others are kept constant.

$z = k x y$

The variable $z$ has joint variation with $x$ and $y .$

Concept

Combined Variation

A combined variation, or combined proportionality, is when one variable depends on two or more variables either directly, inversely, or a combination of both.

$z = \frac{k x}{y}$

The variable $z$ depends on two other variables, $x$ and $y .$ Therefore, this is a combined variation. Any joint variation is also a combined variation.