Compare Represent 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.
The independent variable in this situation is the time spent driving, as this is the variable that can be controlled and manipulated by the family. The dependent variable is the distance traveled, as this is the variable that will be affected by the amount of time spent driving. We know which is which in this situation because the time spent driving will directly influence the distance traveled, making it the dependent variable, while the distance traveled will be determined by the amount of time spent driving, making it the independent variable.
A reasonable speed for the car to travel at for most of the trip would be around 60 miles per hour (mph). This is a common speed limit on many highways and interstates, and it allows for efficient travel while still maintaining safety. Additionally, traveling at this speed would allow the family to cover a significant distance in a relatively short amount of time.
| Time (hours) | Distance Traveled (miles) |
|--------------|-------------------------|
| 0 | 0 |
| 1 | 60 |
| 2 | 120 |
| 3 | 180 |
| 4 | 240 |
| 5 | 300 |
| 6 | 360 |
| 7 | 420 |
| 8 | 480 |
I'm sorry, but I'm unable to draw a graph as I'm a text-based AI. However, I can guide you on how to draw the graph:
- Label the x-axis as "Time (hours)" and the y-axis as "Distance Traveled (miles)".
- Use a scale that allows you to plot the points accurately. For example, if each gridline on the x-axis represents 1 hour, and each gridline on the y-axis represents 60 miles, you can easily plot the points from the table.
- Plot the points from the table on the graph. Start at (0,0) and plot the points (1, 60), (2, 120), (3, 180), (4, 240), (5, 300), (6, 360), (7, 420), and (8, 480).
- Connect the points with a straight line to show the relationship between time and distance traveled during the road trip.
If you have access to a graphing tool or software, you can input the points and generate the graph using the table data provided.
The equation that relates the distance traveled (y) to the time spent driving (x) can be represented as:
y = 60x
In this equation:
- y represents the distance traveled in miles, which is the dependent variable.
- x represents the time spent driving in hours, which is the independent variable.
The coefficient 60 indicates that the car travels at a speed of 60 miles per hour, so the distance traveled is directly proportional to the time spent driving.
To predict how far the car would travel if it drove for 10 hours instead of 8, we can use the equation y = 60x, where y represents the distance traveled in miles and x represents the time spent driving in hours.
Plugging in x = 10 into the equation:
y = 60 * 10
y = 600
Therefore, if the car drove for 10 hours instead of 8, it would travel a distance of 600 miles.
I chose to use the equation method for this prediction because it provides a direct and efficient way to calculate the distance traveled for a given time without the need to construct a new table or plot additional points on the graph. The equation allows for a quick and accurate prediction based on the data and relationship established.
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.