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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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.

$y=kx$

constant of variationor 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
| ||
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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.