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.

Learning Targets

Student Facing

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

CCSS Standards

Building On

Addressing

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.

    Point \(R\) on a coordinate plane, origin \(O\). Horizontal and vertical axis scale negative 4 to 4 by 1’s. The point has coordinates \(R\)(3 comma 2).
  • origin

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

    a coordinate plane