Product Rule for Inverse Variation

Property If $(x 1, y 1)$ and $(x 2, y 2)$ are solutions of an inverse variation, then their products are equal: $x 1y 1 = x 2y 2$. Explanation This is your ultimate shortcut! Since $x 1y 1$ and $x 2y 2$ both equal the same constant, $k$, they must equal each other. This lets you find a missing value in a new pair without first solving for $k$. Just set the product of the first pair equal to the product of the second and solve for the unknown value. Examples If $y=5$ when $x=6$, find $x$ when $y=10$. Using the rule: $(6)(5) = x 2(10) \implies 30 = 10x 2 \implies x 2 = 3$. A teen earns 14 dollars an hour and works 10 hours. How many hours must they work to earn the same amount if their pay is 20 dollars an hour? $(14)(10) = (20)y 2 \implies 140 = 20y 2 \implies y 2 = 7$ hours.