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Linear Plots-Section 3.2
• Graph scatter plots of recursive sequences• Continue to explore the connection between
graphs and tables and how they can be used to solve problems
• Build toward an introduction of the intercept form of a line
Back to the Elevator Problem Do you remember the
simple trick for find the next number on your calculator?
How about if I wanted both numbers to come up together?
You can generate both number sequences on the calculator.
Floor Number
Height (Ft)
0 (Baseme
nt)
-4
1 9
2 22
3 35
4 48
… …
Elevator Recessive Problem Press {0,4} and press Enter
Press {Ans(1) +1, Ans(2) +13} then Enter
Press Enter again to compute the next floor number.
Define variables and plot the data in the table for the first few floors. Does it make sense to connect the points on the graph?
Floor Number
Height (Ft)
0 (Baseme
nt)
-4
1 9
2 22
3 35
4 48
… …
Some Food for Thought…What is the highest
floor with a height less than 200 feet? Is there a floor that is exactly 200 ft high?
How do you get to the next point on the graph?
This is called a linear relationship (because it can form a line)?
Floor Number
Height (Ft)
0 (Basement)
-4
1 9
2 22
3 35
4 48
… …
AnswersThe height of the 15th floor is 191 ft.The height of the 16th floor is 204 feet. No floor is exactly 200 ft. What is the equation of the line that goes
through these points?
On the Road Again page 166
Materials NeededWorksheet: On the Road Again TableTeams: Team Minivan
Team Pickup Truck Team Sports Car
On the Road Again…A family wants to meet for a camping
trip. Mom and Dad are at the campsite when they realize they forgot to pack the tent. Their son and daughter have just left their apartments and cannot be reached by phone. Will Mom and Dad get home before their son and daughter can call from the campsite? When and where will they pass each other on the highway?
On the Road Again…Mom and Dad’s green minivan starts at
the Mackinac Bridge and heads south for Flint on Highway 75. At the same time, their son’s red sports car leaves Saginaw and their daughter’s blue pickup truck leaves Flint. The car and the pickup are heading for the bridge. The minivan travels 72 miles per hour. The pickup travels 66 mi/h. The sports car travels 48 mi/h.
Picture found on page 166.
Complete Steps 3-11 on page 167
Where does the starting value for each routine appear on the graph? How does the recursive rule for each routine affect the points plotted?
Which line represents the minivan? How can you tell?
Where are the vehicles when the minivan meets the first one headed north?
Table We’ll use
http://www.keymath.com/x7033.xml and click on chapter 3: On the Road Again to model this problem.
Where should they be after 5 minutes?How can you tell by looking at the graph
whether the pickup or the sports car is traveling faster? When and where does the pickup pass the sports car?
Complete the Investigate Questions.
Review Assigning HomeworkTurn to page 168 in
the teacher’s edition.Study the various type
of problems presented in this lesson. Study how the descriptions help you see how to assign exercises for further study.
Think about how you would use the suggestions to make up an assignment for your students on this lesson.
Essential: 2-4, 6, 7Performance
Assessment: 8,10Portfolio: 6 Journal: 7, 8Group: 6, 9Review: 1, 5, 11-14
These two tables show the changing depths of two submarines over time.
USS ALBUQUERQUE
Time (s)
0 5 10 15 20 25 30
Depth (ft)
-39 -32 -25 -18 -11 -4 3
USS SPRINGFIELD
Time (s)
0 5 10 15 20 25 30
Depth (ft)
-45 -37.5
-30 -22.5
-15 -7.5 0
Graph both sets of data using L1 (time), L2 (depth for USS Albuquerque), and L3 (depth for USS Springfield).
Describe how the graphs are the same and how they are different. Write a recursive sequence for each submarine that will describe its
time and depth. Explain the meaning of your recursive sequence. Does it make sense to draw a line through the data? Explain. What is the meaning of the points (30,3) for the USS Albuquerque and
(30,0 ) for the USS Springfield? What is the meaning of the points (0,-39) for the USS Albuquerque and
(0, -45) for the USS Springfield?
USS ALBUQUERQUE
Time (s)
0 5 10 15 20 25 30
Depth (ft)
-39 -32 -25 -18 -11 -4 3
USS SPRINGFIELD
Time (s)
0 5 10 15 20 25 30
Depth (ft)
-45 -37.5
-30 -22.5
-15 -7.5 0