Why Vertical Lines Have Undefined Slope

The Organic Chemistry Tutor

This educational video provides a clear mathematical explanation of undefined slope, focusing on why vertical lines result in a division by zero error. The narrator begins by defining what it means for a value to be "undefined" in the context of fractions, specifically when zero appears in the denominator. The video then transitions to the coordinate plane, demonstrating the four types of slope: positive, negative, zero, and undefined. The core of the lesson involves a step-by-step demonstration using the slope formula. By graphing a vertical line and selecting two specific coordinate points, the narrator calculates the slope to prove mathematically why the result is undefined. This is immediately contrasted with a horizontal line, where the calculation results in a slope of zero. This comparison helps clarify a common point of confusion for students regarding zero versus undefined slopes. Finally, the video teaches students how to write linear equations for these special cases without using the slope-intercept form. It offers a practical shortcut by observing which coordinate value (x or y) remains constant along the line. This resource is excellent for Algebra students learning about linear equations, graphing, and the properties of slope, offering both conceptual understanding and procedural fluency.