How to Use Point-Slope Form to Write and Graph Linear Equations

The Organic Chemistry Tutor

A comprehensive tutorial on the Point-Slope Form of linear equations, designed to guide Algebra students from basic definitions to complex applications. The video begins by defining the formula $y - y_1 = m(x - x_1)$ and demonstrating how to substitute values for slope and a specific point. It progresses through a series of scaffolded examples, including identifying slope and points from existing equations, writing equations given specific criteria (slope and a point, or two points), and graphing a line directly from its Point-Slope form. The content covers key algebraic concepts such as handling double negatives when identifying coordinates and calculating slope between two points using the slope formula. The video concludes with a theoretical derivation, showing students exactly where the Point-Slope form comes from by connecting it algebraically to the standard slope formula. This connects procedural knowledge with conceptual understanding. Teachers can use this video as a core instructional tool for Algebra I units on linear equations. It effectively serves as a flipped classroom resource or a review module. The step-by-step nature of the examples allows for natural pause points where students can attempt problems before seeing the solution, making it highly interactive for classroom use.