Predicting from Patterns Activity

Name: ______Date: ______

Moving Straight Ahead

Investigation 2.2, Investigation 2.4, and ACE Question #29

“Moving Straight Ahead” Activity

Project Interactivate - GraphIt

Part A.

Imagine that you are traveling in a van on an interstate highway. You have discovered that the amount of distance you travel is dependant on the amount of time you drive and your speed.

Suppose the van you traveled in averaged a steady 60 miles per hour on the highway. The table below shows the relationship between the time traveled and the distance.

Complete the table

Time (hours) / Distance (miles)
0.5 / 30
1.0 / 60
1.5
2.0
2.5
3.0
3.5

Enter the coordinates pairs into the Data window. Make sure to separate them with commas and hit [Enter] on your keyboard after each pair.
Click on the plot button to plot the points.
Look at the data in the table and on the graph. From this data, write a rule that describes the relationship between distance and time. Use x for the time. (Record the rule below)
Put the rule in the function box
Hit [Enter] on your keyboard to plot the graph.
Are your coordinate points on the line? Explain why or why not.
If the average speed changed to 75 miles per hour, what would you need to change in your rule?
Record the new rule below and then put the rule in the function box. What do you predict will happen to the line when you hit the [Enter] button?
Hit [Enter] on your keyboard to plot the graph. Are the original points below or above the new line?
If the average speed changed to 25 miles per hour, what would your graph look like? Change the rule and check your prediction.

Part B.

Imagine that your school is printing brochures for a school fundraiser. The organizers get estimates from two printing companies.

The costs are given by the following equations:

Company F: C = 15 + .10x

Company G: C = .25x

Where C is the cost in dollars and x is the number of brochures to be printed.

We are going to use the Graphit tool to graph all three of these equations and compare the companies plans.

Go to the Graphit tool online

Uncheck the Use Defaults
Enter the following min, max, and scale values
Type in the equation for the first company then click on the PLOT button
Enter a comma then type in the next equation
Click on the PLOT button

Use the graphs to answer the following:
a) If they print 50 brochures, how much will it cost from Company F? From Company G?

b) If they print 120 brochures, how much will it cost from Company F?
From Company G?
c) For what number of brochures is the cost the same for both companies?

Part C.

Imagine that Ms. Goodhue’s PE class does an experiment to determine their walking rates. Here are the results for three students:

Name / Walking Rate
Terry / 1 meter per second
Jake / 2 meters per second
Sue / 2.5 meters per second

Sue wonders how a person’s walking rate would affect the amount of time it takes her to walk from the school to the frozen yogurt shop.

Find an equation to represent each one of their waking rates. D = Rate (m/s) * Time
a)
b)
c)

Enter the equations into Graphit. Enter the following:

If Terry, Jake, and Sue leave school together and walk toward the frozen yogurt shop at the rates given in the table, how far apart will they be after a minute?
If the yogurt shop is 160 meters from the school, how long will it take each student to walk there?
When Sue arrives at the yogurt shop, how far away will Terry be?
If you are already 40 meters toward the yogurt shop when they start and you are walking at 1.5 meters per second. When will you get there?
List the order of who will arrive when,. Be sure to include yourself and explain how you know.

Part D.

Make up your own problem. Graph it and give your answers below.

From Moving Straight Ahead: Linear Relationships