Linear Equations: y = mx + b — Exploring Intersecting, Parallel, and Perpendicul

① This example dynamically explores the positional relationships between two straight lines—intersecting, parallel, and perpendicular—by adjusting the slope m and y-intercept b. ② Core mathematical concepts include the slope-intercept form of a linear equation y = mx + b, and the conditions for parallelism (equal slopes) and perpendicularity (product of slopes equals -1). ③ Construction highlights: sliders m and b control the parameters of the two lines; line objects L1 and L2 render the graphs; points M and B mark intersections or intercepts, making the effect of parameter changes visually obvious. ④ Suitable for middle and high school students learning linear functions and coordinate geometry, as well as for classroom demonstrations of line families, bridging algebraic expressions and geometric intuition.