Which term describes a quantity that varies directly with two variables, in the form z = kxy?

Which term describes a quantity that varies directly with two variables, in the form z = kxy?

• A. Joint Variation
• B. Direct Variation
• C. Inverse Variation
• D. Proportionality

Answer: (A)

When a quantity depends on two other variables in such a way that increasing either variable increases the quantity, we say it varies with both variables. If z = kxy, z grows with the product of x and y, with k as the constant of proportionality. This situation is called joint variation. Direct variation with two variables would be described as a proportionality to a single variable at a time (not the two-variable product), and inverse variation would involve the reciprocal (like z ∝ 1/(xy)). Proportionality is the broad idea that a constant multiple relates the quantities, but the two-variable case is specifically joint variation.

When a quantity depends on two other variables in such a way that increasing either variable increases the quantity, we say it varies with both variables. If z = kxy, z grows with the product of x and y, with k as the constant of proportionality. This situation is called joint variation.

Direct variation with two variables would be described as a proportionality to a single variable at a time (not the two-variable product), and inverse variation would involve the reciprocal (like z ∝ 1/(xy)). Proportionality is the broad idea that a constant multiple relates the quantities, but the two-variable case is specifically joint variation.