Which equation represents inverse variation, where the product of two variables remains constant?

Which equation represents inverse variation, where the product of two variables remains constant?

• A. x1y1 = x2y2
• B. y = mx + b
• C. xy = k^2
• D. x + y = 1

Answer: (A)

Inverse variation means x and y move in opposite ways so that their product stays the same constant. This is captured by an equation of the form xy = k, where k is a constant. Among the options, the one that directly states the product of x and y is a constant is xy = k^2. Since k^2 is itself a constant, this describes the same inverse-variation relationship: as x changes, y adjusts so that xy remains that constant. The other options don’t express this idea in the same way: a linear equation y = mx + b describes a different relation; x + y = 1 fixes the sum rather than the product; and x1y1 = x2y2 states the product is the same for two specific pairs, which is a consequence of the constant product but not the standard single-equation form.

Inverse variation means x and y move in opposite ways so that their product stays the same constant. This is captured by an equation of the form xy = k, where k is a constant. Among the options, the one that directly states the product of x and y is a constant is xy = k^2. Since k^2 is itself a constant, this describes the same inverse-variation relationship: as x changes, y adjusts so that xy remains that constant. The other options don’t express this idea in the same way: a linear equation y = mx + b describes a different relation; x + y = 1 fixes the sum rather than the product; and x1y1 = x2y2 states the product is the same for two specific pairs, which is a consequence of the constant product but not the standard single-equation form.