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

Linear Plots Materials Needed Graph paper Textbook page 165

Back to the Elevator Problem Floor Number Height (Ft) 0 (Basement) -4 1 9 2 22 3 35 4 48 … 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.

Elevator Recessive Problem Floor Number Height (Ft) 0 (Basement) -4 1 9 2 22 3 35 4 48 … 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?

Some Food for Thought… Floor Number Height (Ft) 0 (Basement) -4 1 9 2 22 3 35 4 48 … 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)?

Answers The 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 Needed Worksheet: On the Road Again Table Teams: 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.

Questions What is each vehicle’s average speed in miles per minute. Minivan: ___ miles per min sports car: ___ miles per min truck: ____ miles per min Which vehicle is the fastest? slowest? Let’s fill in the Highway Distance Table. And graph it. Do you remember how to get a recursive routine for all 3 lists on your calculator? Press {0, 220, 0, 35} and apply the rule. Stop after you have found the 5 minutes. 1.2, 1.1, 0.8

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.

Homework Textbook page 170 #8 a-c #9 a-c #10 a-c #11 #12 #13 Quiz on Friday. Sections 2.7-3.2

Review Assigning Homework Turn 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, 7 Performance Assessment: 8,10 Portfolio: 6 Journal: 7, 8 Group: 6, 9 Review: 1, 5, 11-14

These two tables show the changing depths of two submarines over time. USS ALBUQUERQUE Time (s) 5 10 15 20 25 30 Depth (ft) -39 -32 -25 -18 -11 -4 3 USS SPRINGFIELD Time (s) 5 10 15 20 25 30 Depth (ft) -45 -37.5 -30 -22.5 -15 -7.5

USS ALBUQUERQUE USS SPRINGFIELD 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) 5 10 15 20 25 30 Depth (ft) -39 -32 -25 -18 -11 -4 3 USS SPRINGFIELD Time (s) 5 10 15 20 25 30 Depth (ft) -45 -37.5 -30 -22.5 -15 -7.5