Exploring Linear Functions: Slope, Intercept, and Graph Transformations

① This GeoGebra example dynamically demonstrates how the slope m and y-intercept b of a linear function y = m·x + b affect the line's steepness and position, while also incorporating elements like the unit circle and hyperbola to show connections between different function types. ② Core mathematical concepts include linear functions, slope, intercept, function graphs, unit circle, hyperbola, roots, and frequency distribution, emphasizing function transformations and geometric visualization. ③ Construction highlights: objects m, b, f, a, and c are created; m and b serve as adjustable sliders, f is the linear function expression, and a and c likely support auxiliary graphs (e.g., unit circle or hyperbola). Dragging the sliders updates the graph in real time. ④ Suitable for middle school to high school students learning function basics, and for teachers demonstrating how parameters affect graphs, fostering a visual and algebraic connection.