Which variation describes a quantity that varies jointly with two or more quantities, such as z = kxy?

Which variation describes a quantity that varies jointly with two or more quantities, such as z = kxy?

• A. Direct Variation
• B. Joint Variation
• C. Inverse Variation
• D. Proportional relationship

Answer: (B)

Joint variation describes a situation where a quantity changes in proportion to the product of two or more variables. In z = kxy, z scales with the product of x and y, so increasing either x or y increases z, and the way it changes depends on the product and the constant k. This is a generalization of direct variation, which uses a single variable (y = kx). It’s not inverse variation, which involves a reciprocal (y = k/x). While a proportional relationship means quantities change by a constant multiple, the explicit form z = kxy shows the dependency on the product of two variables, which defines joint variation.

Joint variation describes a situation where a quantity changes in proportion to the product of two or more variables. In z = kxy, z scales with the product of x and y, so increasing either x or y increases z, and the way it changes depends on the product and the constant k. This is a generalization of direct variation, which uses a single variable (y = kx). It’s not inverse variation, which involves a reciprocal (y = k/x). While a proportional relationship means quantities change by a constant multiple, the explicit form z = kxy shows the dependency on the product of two variables, which defines joint variation.