What is referred to as the constant of proportionality?

The constant of proportionality is specifically the number that relates two variables in a direct variation. When two quantities are directly proportional, they change at a constant rate, which can be expressed mathematically as ( y = kx ), where ( k ) represents the constant of proportionality. This constant indicates how much one variable changes when the other variable changes. For example, if doubling one variable results in doubling the other, the constant of proportionality remains consistent.

In contrast, other choices do not accurately define this concept. A variable that changes based on another variable refers to dependent or independent variables within various contexts but does not imply a fixed relationship of proportionality. An equation that keeps a balance of both sides refers more to equality than to proportionality, and the sum of variables in a polynomial pertains to algebraic expressions without regard to their proportional relationships. Understanding this concept is crucial for solving problems involving direct variation, as it provides clarity on how changes in one variable affect another.