Investigating Gradient Using a Line Segment

① This example demonstrates the geometric meaning of the gradient (slope) of a line by using a draggable line segment, showing the ratio of vertical change to horizontal change between two points. ② The core mathematical concept is the slope (gradient), involving coordinates of points, segment length and direction, and an intuitive connection to the tangent ratio in a right triangle. ③ Construction details: The GeoGebra command Segment is used to create the line segment, with objects such as points A, B, C, D, E, segments a, b, c, d, e, f, g, and text objects text1, text2, text3 to label coordinates and slope values; auxiliary line m and perpendicular foot h may be included to dynamically display the slope change. ④ Suitable for upper middle school or early high school students, this interactive tool helps learners understand the definition of slope in linear functions and serves as an introductory demonstration in coordinate geometry.