Your family decides to take a long road trip for the summer. You will be riding in the

Question

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:
- Independent variable: Time (in hours)
- Dependent variable: Distance traveled (in miles)
I know that time is the independent variable because it is what is being controlled or varied during the road trip. The distance traveled depends on how much time 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 (mph). This is a common speed for highway driving and would allow for the car to cover a good amount of distance efficiently.

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:
(Apologies, as a text-based AI, I cannot physically draw a graph.)

Question 5:
The equation relating distance (y) to time (x) can be written as:
y = 60x
Where:
- y stands for the distance traveled in miles
- x stands for the time in hours
In this equation, distance is the dependent variable, represented by y, and time is the independent variable, represented by x.

Question 6:
Using the equation y = 60x, if the car were to drive for 10 hours instead of 8, we can predict the distance traveled by substituting x = 10 into the equation:
y = 60(10)
y = 600 miles
I chose to use the equation because it provides a direct mathematical relationship between time and distance, making it easy to calculate the distance for any given time.