Point-Slope Form of a Linear Function: Defined by Two Points

This GeoGebra example demonstrates how to define a linear function (affine function) using two draggable points, and dynamically displays its point-slope equation. The core mathematical concept is the point-slope form of a linear equation, where a line is determined by a point and its slope, involving slope, intercept, coordinate differences (Δx, Δy), and the angle of inclination. Construction highlights: the Line command creates the straight line, Point commands generate movable points A and B, Segment connects them to visualize Δx and Δy, Angle marks the inclination angle α, and Textfield shows the dynamic equation and slope value. Commands like GetSlope, GetExprASlope, and GetExprBSlope extract expressions for display. Suitable for middle and high school students learning linear functions, line equations, and slope concepts, as well as for classroom demonstrations or self-exploration—dragging the points reveals how the slope and equation change in real time.