The phrase “*y* varies inversely as *x*” or “*y* is **inversely proportional** to *x*” means that as *x* gets bigger, *y* gets smaller, and *vice versa*.

*Inversely proportional* terms can mathematically be represented as:

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Notice how *x* is under a constant *k*.

? Don’t confuse

inverse variationwithinverse functions. Aninverse functionis one that undoes the action of the another function.

The equation y = k over x can also he written as y = k·x^{-1} given the negative exponent rule.

Another form is obtained by multiplying both sides of y = k over x by x, getting:

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Each of these three forms indicate inverse variation. Inverse variation problems are solved by the same methods as for any other **power function**. As before, we can work these problems with or without finding the *constant of proportionality* (k) – question 2 in the video below.