Unit 5, Lesson 7
Graphs of Proportional Relationships
Accelerated 6
Preparation
Lesson Narrative
This lesson introduces an important way of representing a proportional relationship: its graph. Students plot points on the graph from a table of values in a proportional relationship. They see that the graph of a proportional relationship always lies on a line that passes through the origin, .
Then, students interpret points on the graph of a proportional relationship. They make connections between the graph, the equation, and the context modeled by the relationship. Extra attention is given to the meaning of the point on the graph, both in terms of the constant of proportionality in the equation and in terms of a constant rate in the context. As they relate representations and situations, students practice reasoning quantitatively and abstractly (MP2).
- 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.
- Identify the constant of proportionality from the graph of a proportional relationship.
- Interpret (orally and in writing) points on the graph of a proportional relationship.
Let's see how graphs of proportional relationships differ from graphs of other relationships.
Required Materials
Activity 2
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.
For the digital version of the activity, acquire devices that can run the applet.
The coordinate plane is one way to represent pairs of numbers. The plane is made of a horizontal number line and a vertical number line that cross at 0.
Pairs of numbers can be used to describe the location of a point in the coordinate plane.
Point is located at . This means is 3 units to the right and 2 units down from .