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# Geogebra Activity for Applications of Linear Models

- Author:
- dseacrest

**Scenario:**You’re buying books for a book club with several members.

- Amazon charges $8 per book and $5 shipping (no matter how many books you purchase). We’ll let x be the number of books, so A(x) = 8x + 5.
- How much will it cost to buy 4 books? In other words, what is A(x) when x = 4?
- How much will it cost to buy 9 books?
- How many books can you buy if you only have $45? (Hint: make sure your answer is reasonable!)
- What is the domain of the function A(x)? In other words, what values can you reasonably put in for x?
- What is the range of the function A(x)? In other words, what values can you get as answers for A(x)? (This is tricky—I’d suggest describing your answer in words.)
- Click the white dot to the left of A(x) to show the line A(x) = ax+b. Using the mouse or the arrow keys, slide a to 8 and b to 5. What does the result look like? Be as specific as you can.
- Use the line that you created to check your answers to 1a and 1b. Then check your answer to 1c—this may take a bit more thought.

- Barnes and Noble charges $6 per book and $10 shipping (no matter how many books you purchase). We’ll again let x be the number of books.
- How do we write B(x)?
- How much will it cost to buy 4 books? In other words, what is B(x) when x = 4?
- How much will it cost to buy 9 books?
- How many books can you buy if you only have $45? (Hint: make sure your answer is reasonable!)
- What is the domain of the function B(x)? In other words, what values can you reasonably put in for x?
- What is the range of the function B(x)? In other words, what values can you get as answers for B(x)? (This is tricky—I’d suggest describing your answer in words.)
- Click the white dot to the left of B(x) to show the line B(x) = cx+d. Look at the sliders marked c and d. How should you set these so they model the problem? What does the result look like? Be as specific as you can.
- Use the line that you created to check your answers to 2a and 2b. Then check your answer to 2c—this may take a bit more thought.

- You should now have two lines graphed—one for A(x) and one for B(x).
- When is Amazon a better deal?
- When is Barnes and Noble a better deal?
- When will the prices be the same? (There may or may not be a reasonable value where they’re the same. If no reasonable answer exists, explain why.)

- Suppose your parents offer to let you use their Amazon Prime account, so now shipping on the Amazon purchase is free. The books still cost $8 each.
- How should you set sliders a and b to represent this new situation?
- When is Amazon a better deal?
- When is Barnes and Noble a better deal?
- When will the prices be the same? (There may or may not be a reasonable value where they’re the same. If no reasonable answer exists, explain why.)

- Imagine that Amazon has gone out of business. (This may be the hardest part of the entire worksheet.) The campus bookstore wants to compete with Barnes and Noble. They will not charge shipping.
- Click the blue-gray dot to the left of A(x) to hide the line. Click the white dot to the left of C(x) to show the line C(x) = ex+f.
- You can set one slider (e or f) right away, since you know that the bookstore here won’t charge shipping. Which slider, and what should you set it to?
- Change the other slider (either e or f) until the cost of 2 books from Barnes and Noble is the same as the cost of 2 books from the campus bookstore. What slider are you changing, and what do you set it to?
- How much will 2 books cost?
- When is Barnes and Noble a better deal?
- When is the campus bookstore a better deal?