What does 'rate of change' compare in mathematics?

The concept of 'rate of change' in mathematics specifically refers to the change in one variable with respect to another variable, often distinguishing between independent and dependent variables. In option B, it highlights the change in an independent variable to a dependent variable, which accurately captures the essence of how rates of change are used in mathematical contexts, particularly in functions and calculus.

For example, in the context of a graph, the rate of change can be represented by the slope, which depicts how much the dependent variable (often referred to as 'y') changes when the independent variable (often referred to as 'x') changes. This relationship is foundational in understanding concepts like velocity in physics, where the rate of change of position (dependent variable) with respect to time (independent variable) is crucial.

The other options describe concepts that do not align with the standard definition of 'rate of change.' For instance, the focus on constant variables or two independent variables does not directly relate to the fundamental relationship between dependent and independent variables that the rate of change explores. Thus, the correct choice reflects the true nature of what rate of change represents in mathematical analysis.