Direct and Inverse Variation

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What is Direct Variation?

Back

Direct Variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is the constant of variation.

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What is Inverse Variation?

Back

Inverse Variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is the constant of variation.

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What is the constant of variation in direct variation?

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The constant of variation in direct variation is the value of k in the equation y = kx.

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What is the constant of variation in inverse variation?

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The constant of variation in inverse variation is the value of k in the equation y = k/x.

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How can you identify a direct variation from a table of values?

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A table represents direct variation if the ratio of y to x is constant for all pairs of values.

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How can you identify an inverse variation from a table of values?

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A table represents inverse variation if the product of x and y is constant for all pairs of values.

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What is an example of a direct variation equation?

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An example of a direct variation equation is y = 3x.

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What is an example of an inverse variation equation?

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An example of an inverse variation equation is y = 10/x.

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If y varies directly with x and y = 6 when x = 2, what is the constant of variation?

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The constant of variation k is 3, since y = kx implies 6 = k(2) => k = 6/2 = 3.

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If y varies inversely with x and y = 4 when x = 5, what is the constant of variation?

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The constant of variation k is 20, since y = k/x implies 4 = k/5 => k = 4*5 = 20.