Equation of a line through a point parallel to a line

This example demonstrates how to construct the equation of a line passing through a given point and parallel to a given line in the Cartesian plane, with dynamic visualization. The core mathematical concept is coordinate geometry, specifically the condition for parallel lines: equal slopes or proportional direction vectors. The construction uses GeoGebra's Line command, along with objects such as Move, m, c, a, and b, where m and c likely represent the slope and intercept of the given line, and a and b are the coordinates of the point. By moving the point or adjusting parameters, users can observe how the parallel line's equation changes in real time. This is suitable for high school analytic geometry lessons, helping students intuitively grasp the point-slope form and the geometric meaning of parallelism, as well as exploring the effects of slope and intercept on line position.