4 Representations #5: Initial Value and Rate of Change

Investigating the initial value and rate of change.

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5 Representations of Linear Equations
#4: Initial Value and Rate of Change

Background
Completion of 4 Representations #1- #4.

In this activity you are the owner of a taco stand at a street fair. To get set up you need to purchase equipment and supplies. These are items you will only purchase once. You also need to purchase ingredients and disposables. These are items you will use up as you make more taco plates. In other words, the equipment costs remain the same, but the ingredients cost will change as you sell more taco plates.

Inquiry Steps
To start this activity, assume you must purchase \$25 in equipment. After that, ingredients will cost \$2 per taco plate.

Fill in data for rows 2-5 on the spreadsheet with the cost for making 0, 1, 2, and 3 taco plates.
Notice as you put numbers into the spreadsheet, the corresponding points show up on the graph.

Next, use the green sliders for starting value and rate of change to make the green line match the green points.

Question 5-1: Notice the relationship between the numbers on the slider, the equation, the spreadsheet, and the words. Which items seem connected to each other?

Suppose the cost for equipment was \$10 instead of \$25. Put this new data in the purple section of the spreadsheet (rows 9-12) and notice where the purple points are. Now adjust the purple sliders so the line and equation match up with the points.

Compare the data, graphs, equations, and words for the two situations.

Question 5-2: How does changing the price of equipment affect the points in the spreadsheet?

Question 5-3: How does changing the price of equipment affect the location of the points on the graph?

Question 5-4: How does changing the price of equipment affect the equation?

Suppose the cost of ingredients for each taco plate was \$3 instead of \$2. Put this new data in the orange section of the spreadsheet (rows 16-19) and notice where the orange points are. Now adjust the orange sliders so the line and equation match up with the points.

Compare the orange data, graphs, equations, and words with the green.

Question 5-5: How does changing the ingredient costs for each taco affect the points in the spreadsheet?

Question 5-6: How does changing the ingredient costs affect the location of the points on the graph?

Question 5-7: How does changing the ingredient costs affect the equation?

Reflection
Question 5-8: Write a paragraph describing in your own words what you have learned through this exercise.