<span><span><span><span>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 </span>constant.<span> No matter where you check the slope on a straight line, you will get the same answer.</span> </span></span><span><span><span> Non-Linear Functions:</span>When working with <span>non-linear functions, </span>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.<span>FYI: </span>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.</span></span></span>
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 using<span>function notation.</span>