# Lesson 12

Using Graphs to Compare Relationships

### Lesson Narrative

In this lesson students continue their work with interpreting graphs of proportional relationships. An important goal of the lesson is for students to start to interpret the steepness of the graph in terms of the context. They use distance-versus-time graphs to decide which person from a group is going the fastest. They also work with graphs where the scale is not specified on each axis, and realize that they can still use graphs to compare rates.

### Learning Goals

Teacher Facing

• Create and interpret graphs that show two different proportional relationships on the same axes.
• Generalize (orally and in writing) that when two different proportional relationships are graphed on the same axes, the steeper line has the greater constant of proportionality.

### Student Facing

Let’s graph more than one relationship on the same grid.

### Required Preparation

Have available the information from the activity "Tyler's Walk" from the previous lesson.

### Student Facing

• I can compare two, related proportional relationships based on their graphs.
• I know that the steeper graph of two proportional relationships has a larger constant of proportionality.

Building On

Building Towards

### Glossary Entries

• coordinate plane

The coordinate plane is a system for telling where points are. For example. point $$R$$ is located at $$(3, 2)$$ on the coordinate plane, because it is three units to the right and two units up.

• origin

The origin is the point $$(0,0)$$ in the coordinate plane. This is where the horizontal axis and the vertical axis cross.

### Print Formatted Materials

For access, consult one of our IM Certified Partners.