Parallel Lines, Gradient, and Collinearity Dynamic Demo

This GeoGebra example dynamically illustrates the relationships among parallel lines, gradient (slope), and collinearity. It constructs multiple lines and points, using vectors and text labels to visually show that parallel lines have equal slopes and that collinear points satisfy consistent slope conditions. Core mathematical concepts include coordinate geometry, slope of a line, parallel line criteria, and collinearity properties. Construction details: uses Line command to create lines, Point for key points, Vector for direction vectors, If for conditional logic, and Text for dynamic annotations. Objects include A, B, f, C, g, E, u, v, D, F, w, a, b, c, h, i, and multiple text labels. Suitable for high school or early college students learning line geometry, and useful for teacher demonstrations or student exploration. By dragging points or sliders, learners can observe real-time changes in slope values and verify parallel/collinear conditions, strengthening the connection between geometric intuition and algebraic representation.