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What Does that Slope Mean? Activity
The following activity is designed to be used in the classroom to promote discussion; however, it can also be used as a take-home activity.
Ask students to form groups of two or three. Each student will need a graphing calculator and a copy of What Does That Slope Mean Worksheet. This activity is intended to be used with a graphing calculator; however, using a graphing calculator is not necessary to complete the activity. Students may draw each group of linear equations on the same coordinate system using paper and pencil.
Ask students to begin by entering the three equations given in Group 1 into the graphing calculator. Remind students that they must solve all equations for y before entering them into the graphing calculator. It will also be a good idea to change the format of each line so that students can differentiate the graphs of the three lines entered on the graphing screen.
Once all equations have been entered, ask students to go to the graph screen and answer the following questions. If necessary, provide students with additional equations to help answer questions two and three.
  1. How can you describe equations of lines with positive slopes?
  2. As the positive slope increases, what happens to the graph of the line?
  3. As the positive slope decreases, what happens to the graph of the line?
After the group has discussed their answers to the above questions, bring the class together so that one or two groups can share their answers.
Continue this process with Group 2, Group 3, and Group 4 equations on the worksheet. Use the questions below for each respective group.
Group 2:
  1. How can you describe equations of lines with negative slopes?
  2. As the negative slope increases, what happens to the graph of the line?
  3. As the negative slope decreases, what happens to the graph of the line?
Group 3:
  1. How can you describe equations of lines with zero slope?
  2. How are equations of lines with zero slope related to each other?
Group 4:
  1. How can you describe equations of lines with the same slope?
  2. How is this relationship possible?
Instructors can assess this activity by observation and group responses to the questions. If used as a take-home activity, encourage students to sketch the calculators graphing screen for each group on their paper in addition to answering the questions.