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Direct Variation

Direct variation, also known as direct proportionality or proportional relationship, occurs when two variables, and have a relationship that forms a linear function passing through the origin where and

The constant is the constant of variation. It defines the slope of the line. When the relationship is not in direct variation. In the example below, the constant of variation is
A line y=1.5x with a point on the line that can be moved
The constant of variation may be any real number except It is worth noting that the quotient of and is the constant of variation.
Here are some examples.
Examples of Direct Variation
Example Rule Comment
The circumference of a circle. Here, is the diameter of the circle and the constant of variation is
The mass of an object. Here, is the constant density of the object and is the volume.
Distance traveled at a constant rate. The constant of variation is the rate and is the time spent traveling.

Direct variation is closely related to other types of variation.