Inverse Variation

Inverse variation means two quantities are linked so that their product stays constant: xy = k. Because of that, if x gets larger, y must get smaller in the same proportion to keep the product unchanged, which is why the graph bends instead of forming a straight line. The constant k sets the strength of the relationship and can be found from any known pair of x and y values.

Use this when one quantity goes up while another goes down in a way that keeps their product fixed, such as speed and travel time for a fixed distance, or the number of workers and the time needed for a job. It also appears in physics and engineering when one variable must adjust to preserve a constant total or rate.

• Adding x and y instead of multiplying them to find the constant
• Using y = kx, which is direct variation, instead of y = k/x
• Forgetting that if x doubles, y halves only when the relationship is truly inverse variation