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Direct Variation

Concept

Direct Variation

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

y=kxy=kx

The constant kk is called the constant of variation or the proportionality constant, and it defines the slope of the line. When k=0,k=0, the relationship is not a direct variation.
The constant of variation may be any real number except 0.0. Here are some examples.
Examples of Direct Variation
Example Rule Comment
The circumference of a circle C=πdC=\pi d dd is the diameter of the circle and the constant of variation is π.\pi.
The mass of an object m=ρVm=\rho V ρ\rho is the constant density of the object and VV is the volume.
Distance traveled at a constant rate. d=rtd=rt The constant of variation rr is the rate and tt is the time spent traveling.

Direct variation is closely related to other types of variation.