Lesson 3: Characteristics of Graphs
Duration of Days: 2
Lesson Objective
Identify and interpret the x- and y-intercepts of a graph.
Use x- and y-intercepts to graph linear equations.
Analyze the behavior of a function near its intercepts.
What is a vertical intercept?
How do you find it on a graph and in an equation?
What is a horizontal intercept?
What are the behaviors of Graphs
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Lesson Description
This lesson focuses on identifying and interpreting the key "landmarks" of a linear graph. Students will learn to analyze a line to find its most critical components, including:
Intercepts: Locating the x-intercept (where the graph crosses the horizontal axis, y=0) and the y-intercept (where it crosses the vertical axis, x=0).
Trend/Direction: Determining if a graph is increasing (rising from left to right), decreasing (falling from left to right), or constant (horizontal).
Linearity: Distinguishing between a constant rate of change (a straight line) and non-linear patterns.
Point Verification: Confirming that any point (x,y) on the line represents a valid solution to the underlying equation.
Purpose
The purpose of Section 5.3 is to develop analytical observation. By identifying intercepts, students learn to find "starting values" (y-intercept) and "break-even points" (x-intercept) in real-world contexts. Understanding the direction of a graph provides an immediate visual summary of a relationship—such as whether a bank balance is growing or a fuel tank is emptying. This section builds the vocabulary necessary to discuss functions and rates of change in more advanced algebra modules.
Depth of Knowledge (DOK) Level
DOK Level 2
Level 2 (Skill/Concept): Students must move beyond simple recall to categorize and describe the graph. This involves identifying specific coordinates of intercepts from a visual representation and explaining what a "downward" slope means in terms of the relationship between x and y. They are required to compare two different graphs and identify which one has a "higher" intercept or a "steeper" trend.
Class and Online Work
Section 5.3 You Try Page 122
Practice Problems
Textbook with guided class notes and videos