The word "slope" may also be referred to as "gradient", "incline" or "pitch", and be expressed as:
A special circumstance exists when working with straight lines (linear functions), in that the "average rate of change" (the slope) is constant. No matter where you check the slope on a straight line, you will get the same answer. Non-Linear Functions:When working with non-linear functions, the "average rate of change" is not constant.
The process of computing the "average rate of change", however, remains the same as was used with straight lines: two points are chosen, and is computed.FYI: You will learn in later courses that the "average rate of change" in non-linear functions is actually the slope of the secant line passing through the two chosen points. A secant line cuts a graph in two points.When you find the "average rate of change" you are finding the rate at which (how fast) the function's y-values (output) are changing as compared to the function's x-values (input).
When working with functions (of all types), the "average rate of change" is expressed usingfunction notation.
