Line Slope via Run and Rise: Horizontal vs Vertical Change

This example visualizes the geometric meaning of a line’s slope by explicitly using the horizontal change (run) and vertical change (rise) between points on the line. It focuses on the slope as a ratio, rooted in coordinate differences (Δx and Δy) and the idea of “difference over division.” The construction combines geometry and vectors: a line is built with Line, key points are placed with Point, and displacement is represented using Vector so that the rise and run correspond to vector components. A Sequence is used to step through intermediate points or updates along the line, while If controls conditional behavior for displaying or computing stepwise results. Text and step-related objects (e.g., showing run/rise and the computed ratio) guide learners through the calculation. Suitable for middle school through early college levels, especially for teaching slope in coordinate geometry and graph-based reasoning.