In direct variation, what is the relationship between y and x?

In direct variation, the relationship between y and x is defined by a constant ratio. This means that as one variable changes, the other variable changes in a proportional manner, which can be expressed mathematically as ( y = kx ), where k is a constant. This constant tells us how much y changes when x is altered.

For instance, if x doubles, y will also double, maintaining the same ratio ( \frac{y}{x} = k ). This fundamental property distinguishes direct variation from other types of relationships, such as inverse variation or constant products.

The other options do not correctly describe the nature of direct variation. While the first option describes inverse variation, the second refers to a different concept (constant product), and the fourth is a comparison that does not capture any functional relationship between y and x. Thus, the statement that y changes as x changes, with a constant ratio, perfectly encapsulates the essence of direct variation.