Interactive exploration of the linear graph y=mx+c: slope and intercept

This GeoGebra example demonstrates how the graph of the linear function y = mx + c changes as the parameters m (slope) and c (intercept) are adjusted, helping learners visualize the geometric meaning of slope and intercept through a dynamically updated line. Key concepts include linear functions, slope (m), intercept (c), the equation of a line, and the role of intersections in understanding relationships between geometric objects. Construction highlights: Simplify is used to streamline expressions; Intersect finds key intersection points; Point and Line create the essential geometric elements; Textfield (along with text objects such as text1/text2) presents parameter values and explanations; InputBox1/InputBox2 allow direct entry of m and c; button1/button2 control actions, while traceline and traceyint enable dynamic drawing/trajectory-style updates. The scene includes objects like m, c, f, pic1, and auxiliary points/lines (e.g., A, B, g, incr, b) to manage the interactive setup. Suitable for secondary school learners and for classroom demonstrations or inquiry-based activities on graphing and function analysis.