Calculating Average Rate of Change from Graphs and Tables

Miacademy & MiaPrep Learning Channel

This video serves as a bridge between linear algebra concepts and pre-calculus by introducing the concept of Average Rate of Change. While students are likely familiar with finding the constant slope of a line, this lesson addresses how to measure change in non-linear functions where the "slope" is constantly shifting. Through clear visual demonstrations, the narrator explains that while a curve doesn't have a single slope, we can calculate the average rate of change over specific intervals using the familiar slope formula (rise over run). The video explores key themes including the limitations of linear slope on curved graphs, the calculation of average rate of change from both graphical representations and data tables, and the importance of defining specific intervals. It visually demonstrates how drawing a line between two points on a curve (a secant line) represents this average, acknowledging that this is an estimation that ignores the specific ups and downs between the endpoints. The lesson provides step-by-step examples of calculating positive, negative, and zero rates of change. For educators, this resource is an excellent introduction to function analysis for Algebra 1 or 2 classes. It effectively scaffolds learning by starting with prior knowledge (slope of a line) and extending it to more complex functions. The dual focus on visual graphs and numerical tables allows students to practice the skill in multiple formats. It lays essential groundwork for understanding calculus concepts like secant lines and derivatives, making it a valuable conceptual building block for high school math curriculums.