# 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.

### 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.

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.