Inverse Variation

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:


Notice how x is under a constant k.

? Don’t confuse inverse variation with inverse functions. An inverse function is 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:


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.

  • Part 2 and Part 3 can be accessed by following their links.
  • Note that students often misread phrases like square root with square, and vice versa, of a variable as in Part 3; therefore, be cautious as you read through how the function is being modified.