What constitutes direct variation?

Direct variation describes a relationship between two variables where one variable is directly proportional to the other. This means that as one variable changes, the other variable changes in such a way that the ratio between them remains constant.

In the context of the correct response, when it is stated that (y) changes in proportion to (x), it implies that the equation representing this relationship can be formulated as (y = kx), where (k) is a non-zero constant known as the constant of variation. For example, if (x) doubles, (y) will also double, maintaining that consistent ratio, which is the hallmark of direct variation.

This concept is essential in various mathematical applications, as it allows for predictions and relationships to be established based on simple proportionality. The clarity that (y) depends on (x) through a constant ratio fundamentally characterizes direct variation.