Exploring Linear Function Parameters and Their Graphs

This GeoGebra applet demonstrates how the slope m and y-intercept b affect the position and orientation of a linear function y=mx+b. The core mathematical concepts include the algebraic form of linear functions, the geometric meaning of slope (indicating the steepness of a line), and the geometric meaning of intercept (the coordinate where the line crosses the axes). The construction uses Intersect command to find intersection points with coordinate axes, Segment command to draw directed line segments showing slope's geometric interpretation, and Slope command to dynamically calculate and display slope values. Additionally, sliders m and b are used to control parameter changes, allowing students to intuitively observe how the line translates and rotates when parameters vary. Suitable for middle school students learning linear functions in Grade 7, or for reviewing the geometric meanings of slope and intercept.