Exploring Slopes: Parallel and Perpendicular Lines

This GeoGebra example dynamically demonstrates the conditions for two lines to be parallel or perpendicular by adjusting their slopes and intercepts. The core mathematical concepts involve the slope (m) and y-intercept (b) of linear equations, along with the rules that parallel lines have equal slopes and perpendicular lines have slopes whose product is -1. The construction uses the Angle command to display the angle α between each line and the positive x-axis, with objects b_1, b_2 controlling intercepts, m_1, m_2 controlling slopes, and lines f and g as the subjects of study. It is suitable for upper middle school or high school students learning coordinate geometry, and serves as an effective classroom demonstration to bridge visual intuition and algebraic reasoning about line relationships.