Final answer:
A variable rate of change can lead to a non-linear relationship between variables because the rate at which one variable changes is not constant. This can result in a curved line on a graph instead of a straight line.
Step-by-step explanation:
A variable rate of change leads to a non-linear relationship because it means that the rate at which one variable changes is not constant. In a linear relationship, the variables change at a constant rate, resulting in a straight line on a graph. However, with a variable rate of change, the relationship between the variables is not predictable and can result in a curved line on a graph.
For example, let's consider the relationship between distance and time for a car traveling at variable speeds. If the car initially starts slowly, then speeds up, and then slows down again, the rate at which the distance changes (speed) is not constant. This will result in a non-linear relationship between distance and time, as the graph will show a curve instead of a straight line.