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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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 $x.$

$k=xy ⇔y=kx$

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

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

$k=xy⇔y=xk $

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.

$z=kxy$

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

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=ykx $

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.