Understanding slope and y-intercept Student Activity Sheet 3; use with Exploring Comparing slopes and y-intercepts

Transcription

1 1. The parents of the members of the baseball team want to raise money for new uniforms. The parents order team baseball caps and sell them at pep rallies and games. They sell the caps for $10 each. They pay a design fee of $100, plus $3.50 for each baseball cap they order from the manufacturer. Complete these tables to show the money they spend for each cap they order, and the money they collect for each cap they sell. Booster Club Caps Ordered Booster Club Caps Sales Number of caps Number of caps Amount paid Amount collected ordered sold Which amount grows at a faster rate the amount paid or the amount collected? How do you know? 3. What would graphs of these sets of data look like? How do you know? Page 1 of 11

2 4. Create a graph to represent the Booster Club data. Page 2 of 11

3 5. Study the extended scatterplot. How many caps do they need to sell before the club starts to make a profit? 6. Which line on the graph is steeper? Why? Is this what you expected before you graphed the Booster Club data? 7. What is the y-intercept of each line you graphed in question 4? What does each y-intercept represent in the context of the problem situation? Page 3 of 11

4 8. For each data set, find the ratio of the amount paid or collected and the number of caps. What do you notice? Number of caps ordered Amount paid Number of caps sold Amount collected 0 $ $ $ $ $ $ $ $ $ $ $ $ REINFORCE What is a proportional linear relationship and how can you identify one? What does it mean for a quantity to vary directly with another quantity? How is this relationship of direct variation related to a proportional linear relationship? How can you use graphs, tables, and algebraic rules to describe direct variation and proportional linear functions? Page 4 of 11

5 10. Consider the two tables shown. Are the data in each table proportional? Explain your reasoning. a. x y b. x y Page 5 of 11

6 11. Mega Radio Month cost ($) a. What is the rate of change and y-intercept for eradio? b. What is the rate of change and y-intercept for Mega Radio? c. Are either of these proportional relationships? Why or why not? Page 6 of 11

7 12. Create a three-column table comparing the costs of the two radio subscriptions over twelve months. Month eradio Mega Radio Page 7 of 11

8 13. Create a graph of the two linear functions representing eradio and Mega Radio subscription costs. Compare the graphs. 14. How do the graphs confirm what you saw in the tables? Page 8 of 11

9 15. Two friends each won $20 gift cards to an online music store. Amy buys only popular Top 40 songs, which cost $1.50 each. Melissa has different tastes and only buys songs that are not on the Top 40. These songs cost only $0.80 each. Correctly label the line that represents the amount on Amy s card and the line that represents the amount on Melissa s card. 16. REVIEW a. Write an equation for Amy and an equation for Melissa to model the amount of money remaining on the gift card, y, for the number of songs purchased, x. Amy: Melissa: b. How many songs can Amy and Melissa buy with each of their cards? Explain. Page 9 of 11

10 17. eradio is changing its pricing. Their new subscription rate is $2 per month (instead of $3 as it was before), but the company has added a sign up fee of $10. Mega Radio will continue to charge $4 a month with no sign up fee. a. Graph the linear equations that represent the new eradio subscription cost and the Mega Radio subscription cost over time. b. Does eradio s new pricing still represent a proportional relationship? Page 10 of 11

11 c. Create a three-column table comparing the costs of the two radio subscriptions over twelve months. Month eradio Mega Radio 18. REVIEW Write two linear equations that represent eradio and Mega Radio s subscription costs, c, in terms of the number of months, m. 19. eradio's new subscription rate is $2 per month and the company has added a sign-up fee of $10. Mega Radio will continue to charge $4 per month with no sign-up fee. 0 0 to 4 0 to For months, Mega Radio costs less. For a subscription that lasts exactly months, the Internet radio stations' costs are equivalent. For any subscription months or longer, eradio costs less. Page 11 of 11