What does direct variation refer to?

Direct variation describes a specific relationship between two variables where they change together in such a way that the ratio of one variable to the other remains constant. In mathematical terms, if we denote the two variables as (y) and (x), direct variation can be expressed as (y = kx), where (k) is a non-zero constant. This implies that for any change in (x), (y) changes by a proportional amount, thereby maintaining a consistent ratio (y/x = k).

In the context of the options, the correct choice emphasizes the fundamental characteristic of direct variation—this constant ratio is what defines the relationship between the two variables, and it reflects a linear relationship through the origin when graphed. This linear relationship is essentially a straight line that passes through the origin, reaffirming that as one variable increases or decreases, the other does so proportionately.

While other options also describe different types of relationships between variables, they do not encapsulate the specific definition and characteristics of direct variation. For example, stating that one variable is the product of the other does hold some truth but is more aligned with multiplicative relationships rather than highlighting the constant ratio. Similarly, a quadratic function or a general linear equation does