Inverse Variation

Inverse variation

Inverse variation means two quantities change so that their product stays constant. If one quantity increases, the other decreases in a matching way.

1) Write the relationship

Use the form [ y=\frac{k}{x} ] or equivalently [ xy=k ] where k is the constant of variation.

2) Find the constant

If one pair of values is given, substitute them into xy=k to solve for k. For example, if x=4 and y=3, then k=12.

3) Solve for the missing value

Substitute the known value and the constant into the same equation. Then isolate the unknown.

• If you are finding y, use (y=\frac{k}{x}).
• If you are finding x, use (x=\frac{k}{y}).

4) Simplify carefully

Reduce fractions and write the final answer in simplest form.

Check

Multiply your final x and y values. They should give the same constant k. If the product is not constant, recheck your substitution and arithmetic.