This lesson is designed for students who already know how to determine linear equations from a coordinate graph. Its purpose is to illustrate an application of understanding relationships and trends.
To begin the lesson, ask students questions such as:
- What is eBay?
- What is an auction?
- What is a bid?
- What is supply and demand?
- What is the relationship between supply and demand?
- Is there any way you can think of that relationship that may help people make money on eBay?
Allow students to discuss their thoughts and share any personal experiences they may have. The starter questions are a lead-in for the activity sheet. This will allow you to assess students’ current experience and understanding of supply and demand. Clarify any misconceptions of these issues.
Display the Amazing Profit overhead. Hide the equations on the bottom, and give students time to figure out the equations. Review the answers at the bottom and provided additional examples of problems relating to linear equations if necessary.
The Amazing Profit activity sheet explores approximate data from 2006, as collected by a middle school teacher. It has been manipulated to create a linear relationship. You may wish to discuss this with students after the activity. During the lesson, focus on interpreting data.
Read through the introduction together. Then, allow students to complete the activity individually or in pairs, helping them as needed.
Answers
1. PS3 Seller’s Profit: $4,900, $4,400, $3,650, $2,900, $1,900, $1,150
2.
3. y = –250x + 5500
4. y = –250x + 4900
5. x-values represent days the PS3 is on sale on eBay. Negative x-values are not important, because they represent time before the PS3 went on sale.
6. y-values represent money paid for the PS3. Negative y-values for profit represent a loss for the seller. Negative y-values for the Mean Closing Bid line would represent a seller paying a buyer to take the unit off their hands.
7. The lines are parallel, because the profit line will always be $600 less than the closing bid. $600 is the price of the original unit.
8. The lines have negative slope. That means the longer PS3s are selling, the less profit the sellers will get, and the less money the buyers will bid for PS3s.
9. Predictions should be between the 19th and 20th day.
10.a) If the sellers buy PS3s for $600, the lowest price they could set for a profit would be $601.
10.b) Substituting $601 for y in the Mean Closing Bid equation from Question 3 gives a result of approximately 19.6 days.
10.c) The Mean Closing Bid line is just above the x-axis because there is almost no profit.
11. Student answers will vary. Some student responses may be: “Most people who wanted a PS3 could have gotten one,” “Most people can’t afford the extremely high price so they would wait to get one at a store,” “More PS3s make it to the stores so less people want to get one on eBay.”
