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 1
- The independent variable in this situation is the amount of time that has passed, as this is what determines how far the car has traveled.
- The dependent variable is the distance traveled, as it depends on the amount of time that has passed.
- I know which is which because the distance traveled depends on the amount of time that has passed, making it the dependent variable.
Question 2
- A reasonable speed for the car to travel at for most of the trip would be around 60 miles per hour. This is a common speed for highway driving and would allow the family to cover a significant distance in the 8-hour trip.
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
- The graph should have "Time (hours)" on the x-axis and "Distance Traveled (miles)" on the y-axis. The gridlines should be marked at intervals of 1 hour on the x-axis and 60 miles on the y-axis. Plot the points (0,0), (1,60), (2,120), (3,180), (4,240), (5,300), (6,360), (7,420), and (8,480) on the graph.
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
Question 5
- The equation relating distance to time can be written as: 𝑦 = 60𝑥, where 𝑦 represents the distance traveled in miles and 𝑥 represents the time in hours.
Question 6
- Using the equation 𝑦 = 60𝑥, we can predict how far the car would travel if it drove for 10 hours.
- Substituting 𝑥 = 10 into the equation, we get: 𝑦 = 60(10) = 600 miles.
- I chose to use the equation because it allows for a quick and straightforward calculation of the distance traveled after a given time.