Direct variation, also known as direct proportionality, occurs when two variables, $x$ and $y,$ have a relationship that forms a linear function passing through the origin.

The constant $k$ is called the constant of variation or the proportionality constant, and it defines the slope of the line. When $k=0,$ the relationship is not a direct variation. The constant of variation may be any real number except $0.$ Here are some examples.

Examples of Direct Variation
Example	Rule	Comment
The circumference of a circle	$C=\pi d$	$d$ is the diameter of the circle and the constant of variation is $\pi.$
The mass of an object	$m=\rho V$	$\rho$ is the constant density of the object and $V$ is the volume.
Distance traveled at a constant rate.	$d=rt$	The constant of variation $r$ is the rate and $t$ is the time spent traveling.

Direct variation is closely related to other types of variation.