IM 7.2.10 Lesson: Introducing Graphs of Proportional Relationships
Plot the points (0,10), (1,8), (2,6), (3,4), (4,2).
What do you notice about the graph?
Some T-shirts cost $8 each.
Use the table to answer these questions.
What does represent?
What does represent?
Is there a proportional relationship between and ?
Plot the pairs from the above table on the coordinate plane.
What do you notice about the graph?
Here are tables and graphs.
Examine the graphs closely. What is the same and what is different about the graphs?
Sort the graphs into categories of your choosing. Label each category.
Explain why you sorted the graphs the way you did.
Match each tables with a graph.
Trade places with another group. How are their categories the same as your group's categories? How are they different?
Return to your original place. Discuss any changes you may wish to make to your categories based on what the other group did.
Which of the relationships are proportional?
What have you noticed about the graphs of proportional relationships? Do you think this will hold true for all graphs of proportional relationships?
All the graphs in this activity show points where both coordinates are positive. Would it make sense for any of them to have one or more coordinates that are negative?
The equation of a proportional relationship is of the form , where is a positive number, and the graph is a line through . What would the graph look like if were a negative number? You can use the applet below to explore this.