~ 2.10 ~

Introducing Graphs of Proportional Relationships

Learning Targets

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

Notes

One way to represent a proportional relationship is with a graph. Here is a graph that represents different amounts that fit the situation, “Blueberries cost $6 per pound.”

Different points on the graph tell us, for example, that 2 pounds of blueberries cost $12, and 4.5 pounds of blueberries cost $27.

Sometimes it makes sense to connect the points with a line, and sometimes it doesn’t. We could buy, for example, 4.5 pounds of blueberries or 1.875 pounds of blueberries, so all the points in between the whole numbers make sense in the situation, so any point on the line is meaningful.

If the graph represented the cost for different numbers of sandwiches (instead of pounds of blueberries), it might not make sense to connect the points with a line, because it is often not possible to buy 4.5 sandwiches or 1.875 sandwiches. Even if only points make sense in the situation, though, sometimes we connect them with a line anyway to make the relationship easier to see.

Graphs that represent proportional relationships all have a few things in common:

  • Points that satisfy the relationship lie on a straight line.

  • The line that they lie on passes through the origin, (0,0).

Here are some graphs that do not represent proportional relationships:

These points do not lie on a line.

This is a line, but it doesn’t go through the origin.

Vocabulary

origin: In the coordinate plane, the origin is the point (0,0).

Activities

10.2 T-shirts for Sale

Some T-shirts cost $8 each. Use the table to answer these questions.

    1. What does x represent?

    2. What does y represent?

    3. Is there a proportional relationship between x and y?

    4. Plot the pairs in the table on the coordinate plane using the applet to the right.

    5. What do you notice about the graph?

10.3 Matching Tables and Graphs

Open the PDF to the right ->


  1. Match a table with a graph.

  2. Examine the graphs closely. What is the same and what is different about the graphs?

  3. Sort the tables/graphs into categories of your choosing. Label each category. What labels did you use?

  4. Which of the relationships are proportional?

  5. What have you noticed about the graphs of proportional relationships? Do you think this will hold true for all graphs of proportional relationships?

Math 7 Lesson 2.10 Activity 2.pdf

Highlight in Your Notes

Graphs that represent proportional relationships all have a few things in common:

  • Points that satisfy the relationship lie on a straight line.

  • The line that they lie on passes through the origin, (0,0).

Summary

Assignment

Check Google Classroom!