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.