Which relation describes inverse proportionality between x and y?

Which relation describes inverse proportionality between x and y?

• A. y = k/x
• B. y = kx
• C. y = x + k
• D. y = k - x

Answer: (A)

Inverse proportionality means the two variables multiply to a constant: as x gets bigger, y gets smaller in just the right way so that x·y = k. That’s exactly the form y = k/x, where y decreases when x increases, keeping their product the same. For example, if k = 6, then x = 2 gives y = 3, and x = 3 gives y = 2, always with x·y = 6. The other forms describe different relationships: y = kx is direct proportionality (y grows with x), y = x + k is a linear relation with a constant shift, and y = k − x is a linear relation with a negative slope. The inverse relationship has a hyperbolic graph and requires x ≠ 0 and y ≠ 0.

Inverse proportionality means the two variables multiply to a constant: as x gets bigger, y gets smaller in just the right way so that x·y = k. That’s exactly the form y = k/x, where y decreases when x increases, keeping their product the same. For example, if k = 6, then x = 2 gives y = 3, and x = 3 gives y = 2, always with x·y = 6. The other forms describe different relationships: y = kx is direct proportionality (y grows with x), y = x + k is a linear relation with a constant shift, and y = k − x is a linear relation with a negative slope. The inverse relationship has a hyperbolic graph and requires x ≠ 0 and y ≠ 0.