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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.
y=kx
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, when x≠0, is the constant of variation. y=kx ⇔ y/x=k Here are some examples.
| Examples of Direct Variation | ||
|---|---|---|
| Example | Rule | Comment |
| The circumference of a circle. | C=π d | Here, d is the diameter of the circle and the constant of variation is π. |
| The mass of an object. | m= V | Here, 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.