How to Use Slope to Graph Parallel and Perpendicular Lines

Mashup Math

This instructional video provides a clear, step-by-step guide on how to graph parallel and perpendicular lines on a coordinate plane using the concept of slope. The narrator breaks down the geometric definitions of these lines into algebraic rules: parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals (described catchily as "flip and switch"). The visual format uses color-coded lines and clear grid overlays to demonstrate how 'rise over run' is calculated and applied. The content covers two main sections: first defining the slope relationships, and then applying them in two distinct construction problems. In the first problem, viewers learn to construct a line parallel to a given line through a specific point. In the second, they learn to construct a line perpendicular to a given line through a specific point. Each step—calculating the original slope, determining the new slope, and plotting the new line—is animated clearly. For educators, this video serves as an excellent resource for Algebra I and Geometry units on linear equations. It bridges the gap between visual geometry and algebraic calculation. The "flip and switch" mnemonic provides a memorable hook for students struggling with negative reciprocals. The video is ideal for flipped classroom models, remediation for students who missed the lecture, or as a visual anchor during a lesson on coordinate geometry.