Inverse variation

Two quantities vary inversely when their product stays constant: y = k/x, or xy = k, for some nonzero constant k. When one quantity doubles, the other is cut in half. For example, the time to drive 120 miles is t = 120/s: at 60 miles per hour it takes 2 hours, and at 40 miles per hour it takes 3 hours. To solve a problem, find k from one known pair and use it for the next: if y = 6 when x = 4, then k = 24, so when x = 8, y = 24/8 = 3. The graph of y = k/x (with k > 0) is a curve in the first and third quadrants that never touches either axis, unlike direct variation, y = kx, which is a line through the origin.

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