Name__________________________ Date________________________________

Question

Compare Representations Portfolio
Worksheet
Directions: Use this worksheet to record your answers to the road trip activity in
the Compare Presentations Portfolio. When you are finished, save this worksheet
with your answers and submit it for a portfolio grade.
Your family decides to take a long road trip for the summer. You will be riding in the
car while it moves at a fairly constant rate for eight hours to reach your destination.
Record your answers to the questions about this road trip below.
Question 1
Which quantity in this situation is the independent variable?
Which quantity is the dependent variable?
Describe how you know which is which in this situation.
Question 2
What do you think is a reasonable speed for the car to travel at for most of the trip?
Remember to include units of measurement in your answer.
Why did you pick this number?
Question 3
Fill out the table below that shows the amount of time that has passed and how far
you have traveled from 0–8 hours. Make sure to label the quantities on the top row of
the table. Pay attention to which side each quantity should go on.
Question 4
Use the table to plot the points on the graph below. Label the axes with the correct
quantities and use an appropriate scale for the gridlines.
Question 5
Write an equation using the variables 𝑥𝑥 and 𝑦𝑦 that relates the distance to the time.
Label the variables to show what they stand for in the equation. Be careful of which
variable you use for the independent and dependent quantities.
Question 6
Use the table, graph, or equation to predict how far the car would travel if it drove
for 10 hours instead of 8.
Which representation (table, graph, or equation) did you use?
Why did you choose this method?

Answer 1

Question 1
- The independent variable in this situation is the amount of time that has passed, as it is what is changing.
- The dependent variable in this situation is the distance traveled, as it depends on the amount of time that has passed.
- I know which is which because the amount of time that has passed (independent variable) is the cause or input, while the distance traveled (dependent variable) is the effect or output.

Question 2
- A reasonable speed for the car to travel at for most of the trip would be around 60 miles per hour.
- I picked this number because it is a common speed for cars to travel on highways and long road trips.

Question 3

| Time (hours) | Distance Traveled (miles) |
|--------------|--------------------------|
| 0 | 0 |
| 1 | 60 |
| 2 | 120 |
| 3 | 180 |
| 4 | 240 |
| 5 | 300 |
| 6 | 360 |
| 7 | 420 |
| 8 | 480 |

Question 4
(See graph in the portfolio)

Question 5
- The equation relating distance to time is: 𝑦 = 60𝑥
- Where 𝑥 represents the time in hours and 𝑦 represents the distance in miles.

Question 6
- If the car drove for 10 hours instead of 8, according to the equation 𝑦 = 60𝑥, the distance traveled would be 600 miles.
- I used the equation because it allows for a quick calculation without the need to refer back to the table or graph. It provides a clear relationship between the variables.