How can you show the relationship between two variables as a rate?

Answer 1

Here are two ways to look at this: one from algebra, and the other from calculus.

1. Algebra -- You can make a graph with what you want in the denominator plotted on the x-axis, and the measure for the numerator is on the y-axis. The slope is the rate of y per unit x. So if y is distance, and x is time your rate is meters per second, or velocity.
2. Calculus -- Write a function y=f(x) = something. Take the derivative of f(x) with respect to x and that equation is the rate.