Find Average Rate of Change from Graphs via Secant Slopes

This example demonstrates how to compute the average rate of change of a function using its graph. By selecting two points on the curve and drawing the secant line through them, students see that the average rate of change over an interval is exactly the slope of the secant line (i.e., the change in function values divided by the change in input values). The key math concepts include average rate of change, interpreting slope geometrically, and connecting algebraic formulas like (f(x2)−f(x1))/(x2−x1) with graph-based measurements. The typical construction uses: a function graph, two user-chosen points on the graph, the line determined by those two points (the secant), and a computed slope/related numerical value to display the average rate of change. No specific GeoGebra commands were provided in the construct summary, but the essential GeoGebra objects are the function graph, points on the graph, the secant line, and the slope measure derived from the two points. Suitable for middle and high school instruction on functions and graph interpretation, especially when introducing rate/velocity ideas before more advanced topics like instantaneous change.