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Which equation shows inverse variation?

A) y = 2x
B) y = x^2
C) y = 1/x
D) y = 3 + x

1 Answer

1 vote

Final answer:

The equation that shows inverse variation is C) y = 1/x, as it represents a situation where one variable decreases as the other increases.

Step-by-step explanation:

The inverse variation occurs when one variable increases as the other variable decreases at a consistent rate, and is represented mathematically as y = k/x, where k is a nonzero constant. Given this definition, the equation that shows inverse variation among the provided options is C) y = 1/x. The other options given are not representations of inverse variation because they either show a direct variation, or a quadratic relationship or are simply linear equations with a y-intercept. Recognizing the form y = k/x as the defining factor of inverse variation highlights why option C aligns with this concept, distinguishing it from the remaining choices that fail to capture the inverse relationship between variables.

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