What does direct variation describe?

Direct variation describes a specific relationship between two variables where one variable is a constant multiple of the other. This relationship can be expressed in the form ( y = kx ), where ( k ) is a non-zero constant. In this equation, as one variable (x) increases or decreases, the other variable (y) changes in a directly proportional manner, meaning they scale together.

The concept of direct variation highlights that if you double the value of x, the value of y also doubles, and similarly for any other proportional change. This relationship is essential to understanding linear functions where the line through the origin represents perfect direct proportionality between the two variables.

In contrast, other forms provided in the options describe different types of relationships or variations. For example, ( y = k/x ) illustrates an inverse variation, where as one value increases, the other decreases. The equation ( y = mx + b ) represents a linear function that includes a y-intercept, indicating a relationship that does not necessarily pass through the origin, thus not strictly direct variation. Lastly, ( y - y1 = m(x - x1) ) describes the point-slope form of a linear equation; it is useful for defining a line through a specific