Testing for an Inverse Variation

To determine if a data set represents an inverse variation, multiply the corresponding x and y values for each ordered pair. If the product, $xy$, is the same nonzero constant (k) for all pairs of data, it is an inverse variation. The equation is then $y = \frac{k}{x}$.

Data: (x, y) pairs are (2, 15), (5, 6), (10, 3). Check products: $2 \cdot 15 = 30$, $5 \cdot 6 = 30$, $10 \cdot 3 = 30$. It's an inverse variation with $k=30$. Data: (x, y) pairs are (1, 12), (2, 10), (3, 8). Check products: $1 \cdot 12 = 12$, $2 \cdot 10 = 20$. The products are not constant, so this is not an inverse variation.

Are two variables playing on a see saw? To find out, you need to be a data detective! For every pair of (x, y) values you have, multiply them together. If you keep getting the exact same number, that's your constant, k, and you've proven it's an inverse variation. If the products are different, then they aren't playing by inverse rules.