Linear Plots

• 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 NeededGraph paper

You walk into an elevator in the basement of a building. Its control panel displays “0” for the floor number. As you go up, the numbers increase one by one on the display, and the elevator rises 13 feet for each floor. The table shows the floor numbers and their heights above ground level.

Floor Number

Height (Ft)

0 (Baseme

nt)

-4

1 9

2 22

3 35

4 48

… …

Write a recursive routine for the two number sequences in the table. Enter both routines into the calculator.

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

… …

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.

Floor Number

Height (Ft)

0 (Basement)

-4

1 9

2 22

3 35

4 48

… …

On the Road AgainPage 166Materials Needed

The worksheet: On the Road Again Grid

Read the paragraph on page 166 in the investigation.

We’ll use www.keymath.com/DA and click on chapter 3: On the Road Again to model this problem.

We’ll also set up the same problem on our calculator.

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