Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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
Number of caps
Amount paid
ordered
Booster Club Caps Sales
Number of caps
Amount collected
sold
0
0
1
1
2
2
3
3
4
4
5
5
2. 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?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Understanding slope and y-intercept
Date:
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
4. Create a graph to represent the Booster Club data.
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 3 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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
0
1
2
3
4
5
Amount
paid
$100.00
$103.50
$107.00
$110.50
$114.00
$117.50
Number
Amount
of caps
collected
sold
0
$0.00
1
$10.00
2
$20.00
3
$30.00
4
$40.00
5
$50.00
9. REINFORCE What is a proportional linear relationship and how can you identify one?
What does it mean for a quantity to vary directly with another quantity? How is this
relationship of direct variation related to a proportional linear relationship? How can you
use graphs, tables, and algebraic rules to describe direct variation and proportional
linear functions?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
10. Consider the two tables shown. Are the data in each table proportional? Explain your
reasoning.
a.
x
y
1
5
2
6
3
7
4
8
b.
x
y
4
12
6
18
8
24
12
36
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 5 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
11.
Month
0
1
2
3
4
5
6
7
8
9
10
11
12
a. What is the rate of change and y-intercept for eRadio?
b. What is the rate of change and y-intercept for Mega Radio?
c. Are either of these proportional relationships? Why or why not?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 6 of 11
With space for student work
Mega Radio
cost ($)
0
4
8
12
16
20
24
28
32
36
40
44
48
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
12. Create a three-column table comparing the costs of the two radio subscriptions over
twelve months.
Month
eRadio
Mega Radio
0
1
2
3
4
5
6
7
8
9
10
11
12
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 7 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 8 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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.
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 9 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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?
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 10 of 11
With space for student work
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 3; use with Exploring “Comparing slopes and y-intercepts”
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 3
5
6
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.
Copyright 2014 Agile Mind, Inc. 
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 11 of 11
With space for student work