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Investigating Liner Equations Using Graphing Calculator

Activity 5
Real-World Application
Pledge Plans

Objectives:
• Apply the concept of linear equations solve real-world problem
• Use a table to organize information
• Make a graph to display data using heading, labels, and scales
• Use a graphing calculator to see if the graph is correct
• Recognize the relationship among the tables, the graph, the equation, and the
slope of the line
• Identify the y-intercept from a graph or a table

Read the problem carefully and answer all the questions.

Several students from “Help Your School Club” want to raise money for your
school. They are participating in a 10-Kilometer walk-a-thon and need to decide
on a plan for sponsors to pledge money for the walk-a-thon. Chris thinks that
$1.50 per kilometer would be an appropriate pledge. Natalie suggests $2.50 per
kilometer because it would bring in more money. Grace says that if they ask for
too much money, people won’t agree to be sponsors; she suggests that they
ask for a donation of $4.00 and then $0.75 per kilometer.

1. Fill in the table below showing the amount of money a sponsor would owe under
each of the pledge plans. The dollar amounts for 0 Km and 1 Km are filled in as
examples.

Distance 1-10km Money Owed (Dollars)
Chris Natalie Grace
0 0.00 0.00 4.00
1 1.50 2.50 4.75
2      
3      
4      
5      
6      
7      
8      
9      
10      

Use the grid below to answer question #2.

2. On the same coordinate grid, make a graph for each of the three pledge plans.
Use a line to connect the points. Remember to give your graph a title, label your
axes, and show the scale on each axis.

3. Use graphing calculator to check your graph.

Suggested Window
Xmin = 0
Xmax = 10
Xscl = 1
Ymin = 0
Ymax = 25

4. For each of the three plans, describe in your own words, the relationship between
the money earned and the distance walked.

5. Write an equation that can be used to compute the money owed under each
pledge plan. Use M to represent the money owed and d to represent the distance
the student walks.

6. State the slope and the y-intercept for each of the above equations.

7. Describe how increasing the amount of the pledge per kilometer affects the table,
the graph, and the equations.

8. Does the amount of the pledge per kilometer in question #7 relate to the slope of
the line? How does it relate? Explain.

9. Describe what is different about Grace’s plan. What happens in the table, the
graph, and the equation when Grace’s plan is introduced?

Challenge:
10. Write your own pledge plan and sketch its graph. Make your own axes and show
the labels and scale. Use the graphing calculator to check your graph.

Activity 6
Scatter Plot and Line of best Fit

Objectives:
• Using the graphing calculator, graph a scatter plot of two related variables.
• Graph the” line of best fit”.
• Interpolate and extrapolate points in your data.

Collect data of the height (in inches) and the weight (in pounds) of each
member in your family. Make a table of your data and bring it to math class (At
least 8 entries).

1. Make a scatter plot of your data on a grid paper. Remember to show a title, label
and scale on each axis. Draw the line of best fit.
2. Use the graphing calculator and graph the scatter plot for your data.
3. Follow the graphing calculator manual or your teacher’s instruction to show the line
of best fit on your calculator’s screen.
4. Compare the graph of the calculator with your graph on the grid paper. Are they the
same? ________. Are they different? Why? ____________________________
5. Use the “trace” feature and the line of best fit to interpolate and extrapolate the
weight and height of an absent (or a virtual) family member. Examples of what you
need to find are explained below.

Interpolate:
What would be the weight of a family member whose height is in between the
shortest and the tallest of your family? (The point is somewhere inside your data)

Extrapolate:
What would be the weight of a family member whose height is shorter than the
shortest, or taller than the tallest family member? (The point is somewhere
outside your data).

6. Use the “linear regression” feature of the graphing calculator to find the slope and yintercept
of the line of best fit.
7. Write the equation of the line of best fit. _______________________________

Challenge:
Show on a piece of paper, how you would use the slope and y-intercept of the line of
best fit to interpolate and extrapolate the height and weight of the two virtual family
members in question #4. Did you get the same result?

Criteria

Points
  4 3 2 1  
Assignment
Completeness
All items
attempted.
90% of items
attempted.
At least 50%
of all items
attempted.
Less than 50%
of all items
attempted.
____
Accuracy All items are
correct.
90% of items
are correct.
Between 50%
and 90% of
items are
correct.
Less than 50%
of all items are
correct.
____
Graph
Neatness
All sketches /
graphs are neatly
drawn. All lines
are straight, and
all axes are
labeled with
correct scale
showing.
90% of graphs
are neatly
drawn, with
straight lines,
labeled axes
and correct
scale showing.
At least 50%
of graphs are
neatly drawn,
with straight
lines, labeled
axes and
correct scale
showing.
Less than 50%
of graphs are
neatly drawn,
with straight
lines, labeled
axes and
correct scale
showing.
____
Demonstrated
Knowledge
Shows complete
understanding of
the questions,
mathematical
ideas, and
processes.
Shows
substantial
understanding
of the problem,
ideas, and
processes.
Response
shows some
understanding
of the
problem.
shows a
complete lack
of
understanding
for the problem
____
Requirements Goes beyond the
requirements of
the problem.
Meets the
requirements of
the problem.
the problem.
Does not
meet the
requirements
of the
problem.
  ____
Legibility Legible
handwriting,
typing or printing.
Marginally
legible
handwriting,
typing, or
printing.
Writing is not
legible in
places.
Writing is not
legible.
____
        Total -->"  

Teacher’s comments: ________________________________________________

1. What did you learn from these activities?
2. What did you like best about these activities?
3. What was most difficult about these activities?
4. What would you do differently next time?
5. What do you think your teacher should do differently next time