In the previous lesson students learned that the graph of a proportional relationship lies on a line through the origin. (Students should come to use and understand “the origin” to mean \((0,0)\).) In this lesson, they start to make connections between the graph and the context modeled by the proportional relationship, and between the graph and the equation for the proportional relationship. Given a graph, they think about what situation it might represent and learn the importance of being precise about saying which quantities are represented on each axis (MP6). They interpret the meaning of the point \((1,k)\) on the graph both in term of the constant of proportionality \(k\) in the equation \(y = kx\) and in terms of a constant rate in the context.
Lesson overview
 11.1 Warmup: What Could the Graph Represent? (5 minutes)

11.2 Activity: Tyler's Walk (15 minutes)
 Includes "Are you Ready for More?" extension problem

11.3 Activity: Seagulls Eat What? (15 minutes)
 There is a digital applet in this activity.
 Lesson Synthesis
 11.4 Cooldown: Filling a Bucket (5 minutes)
Learning goals:
 Create the graph of a proportional relationship given only one pair of values, by drawing the line that connects the given point and (0, 0).
 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.
Learning goals (student facing):
 Let’s read stories from the graphs of proportional relationships.
Learning targets (student facing):
 I understand the information given by graphs of proportional relationships that are made of up of points or a line.
 I can find the constant of proportionality from a graph.
 I can draw the graph of a proportional relationship given a single point on the graph (other than the origin).
Required materials:
 rulers
Glossary:
 Access the complete Grade 7 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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