Q:
# What are some real-world examples of direct variations?

Direct variation exists when a worker is paid based on the number of hours worked. Another example of a direct variation is a taxi fare that varies according to the distance traveled. Direct variation occurs with two variables when the ratio of their values always remains the same. For example, if the value of A is always twice as much as B, they vary directly.

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Direct variation can be expressed as an equation, an algebraic expression or a geometric expression. To illustrate the concept of direct variation as an equation, take the equation y/x = 6. Y varies directly with X, with 6 being the constant in the equation. From the equation, it can be determined that Y is always six times greater than X. The equation y = kx is an example of an algebraic equation that illustrates direct variation. Both Y and X are always multiplied by the same amount. This equation is a linear equation. In addition to direct variations, other relationships between numbers and variables that remain constant exist in the mathematical world. Variables A and B are said to be inversely related to each other when A varies as the reciprocal of B. Variables can also be jointly related.

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