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One question, multiple parts. The graphs don't necessarily need to be done on Desmos, they can be written out. Thank you!

Anticipatory Problem Set 4: Linear Functions 1. Skate Rental (from Algebra for Elementary and Middle School Teachers: An Inquiry Approach, Stump, Roebuck \& Bishop, 2009): Fifth graders voted to go skating to celcbrate the end of state testing. The planning committee received the following quotes: Roll-Away Skates charges $5 per person Wheelie's Skates and Stuff charges $100 plus $3 per person Which company should the committee choose if they want to keep their costs to a minimum? Explain how you made your choice. A variety of representations can be used to represent this situation. a. For each company, write an equation to show the relationship between the number of people and the cost. i. What is the independent variable? ii. What is the dependent variable? iii. How can these equations be used to determine which company would be best? b. Graph both equations below. You are welcome to use Desmos and insert a picture of the graph(s). i. What range of values did you use for the rental cost? ii. How did you select these ranges? iii. On which graph is the point (8,40) ? What does this point mean in terms of the cost to rent skates? iv. On which graph is the point (8,124) ? What does this point mean in terms of the cost to rent the skates? v. Find the point of intersection of the two graphs. What does this point mean in terms of the cost to rent skates? c. Create a table to show the relationship between the number of people and the cost for each company. How does a table help you see which company offers the better deal? d. Can you say for sure which company provides the best deal for the fifth graders? Why or why not? e. Suppose it is one class of 30 students. Which company would you choose? Why? How can you determine this from the equations, the graph, and the table? f. What if 100 students were going skating? Which company would you choose? Why? g. Is there a number of students for which the two companies cost the same? How can you identify this number using the equations, the graph, and the table? h. If your budget for skate rental is $350, how many pairs of skates can you rent from each company? i. For cach of the two companies, the relationship between the number of people and the cost is an example of a linear function. Why is this called a linear function? j. When the equations of linear functions are written in the form y=mx+b, the variables m and b are parameters. Their values determine the relationship between x and y. i. What are the values of m in each equation? ii. What do these values of m mean in terms of the cost to rent skates? iii. How do the values of m appear in the graphs? iv. How do the values of m appear in the table? v. What are the values of b in each equation? vi. What do these values of b mean in terms of the cost to rent skates? vii. How do the values of b appear in the graphs? viii. How do the values of b appear in the table? k. What are some advantages and disadvantages of using equations, graphs, and tables to examine linear situations? 1. Summarize what you know about the graph of a linear equation of the form y=mx+b

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