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 a non-zero constant.

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What is Inverse Variation?

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Inverse Variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as xy = k, where k is a non-zero constant.

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How do you identify Direct Variation from a table of values?

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In Direct Variation, if you double one variable, the other variable also doubles. The ratio of the two variables remains constant.

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How do you identify Inverse Variation from a table of values?

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In Inverse Variation, as one variable increases, the other variable decreases such that their product remains constant.

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What is the formula for Direct Variation?

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The formula for Direct Variation is y = kx, where k is the constant of variation.

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What is the formula for Inverse Variation?

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The formula for Inverse Variation is xy = k, where k is the constant of variation.

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If y varies directly with x and y = 10 when x = 2, what is the constant of variation?

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The constant of variation k = y/x = 10/2 = 5.

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If x varies inversely with y and x = 4 when y = 2, what is the constant of variation?

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The constant of variation k = xy = 4 * 2 = 8.

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What is a real-world example of Direct Variation?

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A real-world example of Direct Variation is the relationship between distance and time when traveling at a constant speed.

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What is a real-world example of Inverse Variation?

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A real-world example of Inverse Variation is the relationship between the speed of a vehicle and the time it takes to reach a destination; as speed increases, time decreases.