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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. 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.

1 answer

To relate distance and time for your road trip, we can use the equation for distance, which is given by:

\[ y = r \cdot x \]

where:

  • \( y \) represents the total distance traveled (in miles or kilometers),
  • \( x \) represents the time spent traveling (in hours),
  • \( r \) is the rate of travel (in miles per hour or kilometers per hour).

In this context, since you will be traveling for 8 hours, your time \( x \) will range from 0 to 8, and the distance \( y \) will depend on the speed at which you are traveling.

For example, if you are traveling at a constant speed of \( r \) miles per hour, you can substitute that value into the equation. Here is how that would look:

  1. Identify the speed: Let's say you are traveling at a speed of 60 miles per hour.
  2. Equation: The equation becomes: \[ y = 60 \cdot x \]

This equation means:

  • If \( x = 0 \) (you haven't started the trip), \( y = 0\) miles.
  • If \( x = 1 \) (after 1 hour), \( y = 60\) miles.
  • If \( x = 8 \) (after 8 hours), \( y = 480\) miles.

Independent and Dependent Variables:

  • The independent variable is \( x \) (time in hours) because it's what you can control or choose during your trip.
  • The dependent variable is \( y \) (distance in miles) because it depends on the time spent traveling at the constant speed.

In conclusion, the relationship between distance and time on your road trip is captured in the equation \( y = r \cdot x \) with the specified values for your speed.