Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
1. Shawna earns $10 each week helping her grandmother with housework. Instead of
spending the money, Shawna decides to save her money in the bank. Complete the table
to show the relationship between the number of weeks she works and the amount of
money she saves.
Time in weeks (t)
Process
Amount saved (a)
1
$10
$10
2
3
4
$10 + $10 or $10(
)
$10 + $10 + $10 or
$10(
)
$10(
)
5
(
)
6
(
)
t
(
)
=
2. Now, use the data in the table to construct a graphical representation of her problem
situation. Does Shawna’s savings vary directly with the time in weeks worked? Explain your
answer.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
3. In questions 1 and 2, you created a table and graph to represent Shawna's savings
situation. You also wrote a rule, where a represents the amount of money saved and t
represents the time in weeks. Each week, the amount of money in Shawna’s savings
account increases by $10. Where do you see this constant rate of change in each
representation?
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
4. Manuel worked all summer at an amusement park and saved $1050. At the end of the
summer, he stopped putting money into the account and instead began making weekly
withdrawals. Manuel made this table to represent the activity in his account. Describe
precisely what is happening to the amount of money in Manuel's savings account. Does
Manuel’s savings amount vary directly with the time in weeks worked? Explain your
answer.
Time in weeks
0
1
2
3
4
5
6
Amount in savings
$1050
$1000
$950
$900
$850
$800
$750
5. In the table, you can see 6 weeks of Manuel's spending. Study the pattern in the table, and
then write a linear function rule that you could use to find out how much Manuel will still
have in his savings account after 10 weeks or 20 weeks.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
6. Assume that Manuel's spending rate remains the same for several more weeks. Use your
rule to calculate how much money Manuel will have in his savings account after 15 weeks.
7. Make a scatterplot of the data shown in the table in question 5. Then graph the function
rule by drawing a line through the points you have plotted.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
8. What will happen to the table, the function rule, and the graph if Manuel spends $100
each week instead of $50 each week? How do you know?
9. You can use triangles to show that the slope of a line is the same for any pair of points on
the line. Consider the diagram, then explain how you know that the slope of a line is the
same between any two points on the line.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
10. REINFORCE Determine the rate of change for the given data.
Time (sec)
0
2
4
6
Distance (ft)
8
16
24
32
11. REINFORCE Describe three different ways you could calculate the rate of change for the
data shown on the graph.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
12. REINFORCE Griffin works at the local burger stand. When he works 10 hours a week, he
makes $80. When he works 15 hours a week, he makes $120. If you graph the line that
contains these two points, what will be the value of the slope? What does the slope
represent in this situation?
13. REINFORCE In his spare time, Griffin helps his brother Grady study for his multiplication
test. When Grady practiced multiplication for 10 minutes, he only got 5 problems correct.
When he practiced for 30 minutes, he got all 15 problems correct. If you graph the line
that contains these two points, what will be the value of the slope? What does the slope
represent in this situation?
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
14. REINFORCE Elisabeth bought a new type of dry food for her large dog. The side of the bag
contained this table. If you graph the information in the table, what will be the value of
the slope of the graph? What will the slope represent in this situation?
Weight of dog
(in pounds)
50
100
150
Amount of
food (in cups)
2
3
4
15. REINFORCE Mrs. Snow has been tracking her expenses at
her snow-cone stand. The number of cones sold and the
expenses are shown in the table. If you graph the
information in the table, what will be the value of the
slope of the graph? What does the slope represent in this
situation?
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Number of
cones sold
80
90
100
110
120
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Expense
in dollars
147
156
165
174
183
Student:
Class:
Date:
Understanding slope and y-intercept
Block 8 Student Activity Sheet
16. REINFORCE A serving of oatmeal requires a specific ratio of water to oats. This
information is represented in the graph.
a. What do the slope and y-intercept represent in this situation?
b. Use the graph to fill in the table.
Cups of oats
0.5
1
1.5
2
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Cups of water
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