4 Representations of Linear Equations
#2: Rate of Change in Words
Background
Completion of 4 Representations #1.
Inquiry Steps
Click on button 1. You will see a description of a rate of change, and on the graph you will see a line that represents that rate of change. Move the sliders so that Δy and Δx match the given situation. When they match you will see the equation appear at the bottom of the yellow window.
Next, notice the spreadsheet has five data points, all (0, 0). Leave the first point (row 2) at (0, 0), but adjust the data for the other points so the points will match the described situation. As you change the values for the data points, you will see the points move on the graph area. Keep adjusting points until they all appear on the line.
Question 2-1 through 2-10: Write the values for Δy and Δx, the equation, and the five data points for each of the ten situations.
Example: 1. Δy=6 Δx=7, y = 6/7x, (0, 0) (7, 6) (14, 12) (21, 18) (28, 24)
Question 2-11: Describe the relationship between Δy and the values in column B of the spreadsheet.
Question 2-12: Describe the relationship between Δx and the values in column A of the spreadsheet.
Question 2-13: On the situation from button #2, the words say the rate of change is 10/6 but the equation appears as y=5/3 x. Explain why this happens. Imagine someone challenges you to prove that these two rates of change are the same. Without reducing the fraction, how could you demonstrate these two rates are the same? If you can think of more than one way, write each one.
Reflection
Question 2-14: Write a paragraph describing in your own words what you have learned through this exercise.
Question 2-15: What would you change about this exercise to make it better?
Question 2-16: I found this: 1-Very interesting, 2-Interesting, 3-OK, 4-Boring, 5-Very Boring
Question 2-17: I learned: 1-A lot, 2-Something, 3-Not much, 4-More confused than before.