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Student Page 2.5.3 Where Else Do You Use Proportional Reasoning? Proportional Linear Function Example
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We have seen that the relationship between distance and time is proportional when speed is constant. We have also seen that proportional reasoning arises in rescaling recipes. What other relationships are proportional? Work with your group to identify at least 3 other proportional relationships. Complete Where Else Do You Use Proportional Reasoning? Proportional Linear Function Example for each relationship your group identifies.

Once you have completed the above, look for common properties among the examples you found. With your group, answer these questions:

  • What is a proportional relationship?

  • What properties do all proportional relationships have in common?

  • For a proportional relationship, how can you find the slope from:

    • A table?

    • A graph?

    • An equation?

    • A context?

Choose one or two of your group's proportional relationships to share with the class. Post them as directed by your teacher. Groups will cycle through them and indicate with a checkmark if they agree with your work. They will draw a circle if they have a question about your work.

Title:

Description

Independent variable (description and variable):

Dependent variable (description and variable):

1.

Create a table as demonstrated in Table 2.5.3.1. Briefly describe the independent variable in the cell above \(x\text{.}\) Briefly describe the dependent variable in the cell above \(y\text{.}\) Choose eight reasonable \(x\)-values (not all consecutive); write them in the first column of the table. Find the corresponding \(y\)-values; write them in the second column of the table.

Table 2.5.3.1. Table for a Proportional Linear Function
  
  
  		   
  
  
\(x\) \(y\)
             
             
             
             
             
             
             
             
Figure 2.5.3.2. Blank Graph for a Proportional Linear Function

2.

Plot the data on Figure 2.5.3.2. Label accurate scales for both \(x\) and \(y\) so that you use most of the graph. Write titles on each axis to show what quantity each axis represents.

3.

Find an equation.

(a)

How can you get the value of the dependent variable from the value of the independent variable?

4.

Answer these questions on the back of this page.

(a)

What is the slope of the graph?

(b)

How is the slope of the graph related to the equation?

(c)

How is the slope of the graph related to the table?

(d)

How is the slope of the graph related to the context?