Direct variation, also known as direct proportionality or proportional relationship, occurs when two variables, $x$ and $y,$ have a relationship that forms a linear function passing through the origin where $x\ne 0$ and $y\ne 0.$ The constant $k$ is the constant of variation. It defines the slope of the line. When $k=0,$ the relationship is not in direct variation. In the example below, the constant of variation is $k=1.5.$ The constant of variation may be any real number except $0.$ It is worth noting that the quotient of $y$ and $x$ is the constant of variation. Here are some examples.

Examples of Direct Variation
Example	Rule	Comment
The circumference of a circle.	$C=\pi d$	Here, $d$ is the diameter of the circle and the constant of variation is $\pi .$
The mass of an object.	$m=\rho V$	Here, $\rho$ 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.