Lesson 5

More Linear Relationships

Lesson Narrative

The previous lesson looked in depth at an example of a linear relationship that was not proportional and then examined an interpretation of the slope as the rate of change for a linear relationship. In this lesson, slope remains important. In addition, students learn the new term vertical intercept or \(y\)-intercept for the point where the graph of the linear relationship touches the \(y\)-axis. 

In the first activity, students match situations to graphs and then interpret different features of the graph (slope and \(y\)-intercept) in terms of the situation being modeled (MP2). In the second activity, students analyze a common error, studying what happens when the slope and \(y\)-intercept are interchanged. This provides an opportunity to see how the \(y\)-intercept and slope influence the shape and location of a line: the \(y\)-intercept indicates where the line meets the \(y\)-axis while the slope determines how steep the line is. 

Interpreting features of a graph or an equation in terms of a real-world context is an important component of mathematical modeling (MP4).

Learning Goals

Teacher Facing

  • Describe (orally and in writing) how the slope and vertical intercept influence the graph of a line.
  • Identify and interpret the positive vertical intercept of the graph of a linear relationship.

Student Facing

Let’s explore some more relationships between two variables.

Required Preparation

Print and cut up slips from the Slopes, Vertical Intercepts, and Graphs blackline master. Prepare 1 set of cards for every 2 students.

Learning Targets

Student Facing

  • I can interpret the vertical intercept of a graph of a real-world situation.
  • I can match graphs to the real-world situations they represent by identifying the slope and the vertical intercept.

CCSS Standards

Building On


Glossary Entries

  • vertical intercept

    The vertical intercept is the point where the graph of a line crosses the vertical axis.

    The vertical intercept of this line is \((0,\text-6)\) or just -6.

    A graph of a line with a vertical intercept of -6

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