you take a 10-day trip across the country by car. at the beginning of the trip you zero the odometer and every evening you write down the odometer reading. at the end of the trip, you make a graph of cumulative miles traveled vs. the day the measurement was taken

Question

Which of the following do you think is true?
a. The mileage is the independent variable and the day is the dependent variable.
b. The day is the independent variable and the day is the dependent variable.
c. Neither variable is independent or dependent.

the odometer which measures the number of miles traveled based on the rotation of the car's wheels. This car traveled 91,308 miles.

Explain your reasoning

Answer 1

In the context of the scenario you've described, the correct option is:

b. The day is the independent variable and the mileage is the dependent variable.

Here's the reasoning behind this:

1. Independent Variable: An independent variable is one that you can control or that stands on its own; it is the variable you think might be influencing something else. In this case, the day of your trip (from Day 1 to Day 10) is independent because it progresses regardless of how many miles you travel. You set your schedule in terms of days.

2. Dependent Variable: A dependent variable is one that you measure in an experiment or analysis. In this scenario, the cumulative miles traveled (which you record each evening) depends on the day of the trip. Every day you travel more miles, so the cumulative mileage changes based on how many miles you drive on that day.

3. Graphing Context: When you graph the cumulative miles traveled (dependent variable) against the day (independent variable), the x-axis typically represents the independent variable (the days), while the y-axis represents the dependent variable (the cumulative mileage).

In summary, the day is the independent variable because you can independently determine the sequence of days, while the mileage is the dependent variable because it changes based on your travel for each respective day.