Lesson 4: Horizontal and Vertical Lines

How do we use an equation to find ordered pairs that satisfy the equation?

Ordered pair; Coordinates (x, y); Equation; Graph

NA

Lesson Description: This lesson focuses on the unique properties and equations of lines that are parallel to the axes. Students will learn to distinguish between: Horizontal Lines: Equations in the form y = b. These lines have a constant y-value regardless of the x-value, resulting in a slope of zero. Vertical Lines: Equations in the form x = a. These lines have a constant x-value regardless of the y-value, resulting in an undefined slope. Students will practice identifying these lines from their equations, plotting them on the Cartesian plane, and articulating the difference between a "zero" slope and an "undefined" slope.
Purpose : The purpose of Section 6.4 is to address conceptual "dead zones" in algebra. Students often struggle with x = a and y = b because they expect two variables in every line. By isolating these cases, students learn that a single-variable equation in a two-variable system represents a set of points where one coordinate is fixed. This understanding is vital for defining boundaries in linear programming, understanding constraints in physical sciences, and correctly identifying intercepts in more complex functions.
Depth of Knowledge (DOK) Level
DOK Level 1 & 2
Level 1 (Recall & Reproduction): Memorizing that y = constant is horizontal and x = constant is vertical. Identifying the slope of a horizontal line as 0 and a vertical line as undefined.
Level 2 (Skill/Concept): Graphing these lines from given equations and writing the equation of a line when given a graph or a single point (e.g., "Write the equation of the horizontal line passing through $(2, -5)"). Students must also explain why the slope of a vertical line is undefined using the slope formula.

Class and online work

Use practice problems 5-15, pages 144-147 to assess students' understanding of the lesson concepts