Lesson 3: Intercepts

How do we find the intercepts of a linear equation?

How do we use intercepts to easily plot a linear equations?

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

NA

Lesson Description: This lesson focuses on the Intercept Method for graphing linear equations, particularly those in standard form (Ax + By = C). Students will learn the algebraic definitions of the "starting points" on a graph: The x-intercept: The point where the graph crosses the x-axis, found by setting y = 0.The y-intercept: The point where the graph crosses the y-axis, found by setting x = 0.The "Cover-up" Method: A mental math strategy for solving for one variable when the other is zero. Graphing via Intercepts: Plotting these two specific points and connecting them to form a line (and identifying when a third "test point" is needed, such as when the line passes through the origin).
Purpose: The purpose of Section 6.3 is to promote mathematical efficiency. In many real-world applications, the intercepts represent the most important data points—the "initial value" (y-intercept) and the "zero-out point" (x-intercept). By focusing on these points, students learn a faster way to graph equations in standard form without having to rearrange them into slope-intercept form. This section also reinforces the fundamental concept that points on the axes always have one coordinate equal to zero, a common point of confusion for beginning algebra students.
Depth of Knowledge (DOK) Level
DOK Level 1 & 2
Level 1 (Recall & Reproduction): Defining what an intercept is and remembering that x=0 for the y-intercept and y=0 for the x-intercept.
Level 2 (Skill/Concept): Algebraically calculating the intercepts for a given equation and using them to construct a graph. Students must also recognize when the intercept method is not sufficient (e.g., when the x and y intercepts are the same point at the origin) and decide to use a third point to determine the line's direction.

Class and online work

Use practice problem 16, page148 to assess students' understanding of the lesson concepts