# Lesson 10

Introducing Graphs of Proportional Relationships

### Lesson Narrative

This lesson introduces an important way of representing a proportional relationship: its graph. Students plot points on the graph from tables, and, by the end of the lesson, start to see that the graph of a proportional relationship always lies on a line that passes through $$(0,0)$$. They match tables and graphs of given situations and articulate their reasons for each match (MP3).

### Learning Goals

Teacher Facing

• Compare and contrast (orally) graphs of relationships.
• Generalize (orally and in writing) that a proportional relationship can be represented in the coordinate plane by a line that includes the “origin” or by a collection of points that lie on such a line.
• Justify (orally) that a table and a graph represent the same relationship.

### Student Facing

Let’s see how graphs of proportional relationships differ from graphs of other relationships.

### Required Preparation

Prepare Matching Tables and Graphs activity by printing one copy for each group of 2 students and cutting them up ahead of time. Prepare a few copies of an answer key and place them in envelopes for students to access to check their work when they finish.

### Student Facing

• I know that the graph of a proportional relationship lies on a line through $(0,0)$.

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.

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