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Concept

# Direct Variation

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.

$y=kx$

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.