To determine the correct equation and whether the situation is proportional or nonproportional, we need to analyze the information given:
- The family has already traveled 500 miles.
- The next day, they will travel at an average speed of 70 miles per hour.
The total distance they travel (y) after driving for x hours on the next day can be modeled in the following way:
- The distance traveled on the next day at 70 mph would be \( 70x \).
- Adding the initial 500 miles gives us the total distance: \[ y = 70x + 500 \]
Now, regarding whether this is a proportional or nonproportional situation:
- A proportional relationship would pass through the origin (0,0) and would mean that y is directly proportional to x.
- A nonproportional relationship includes a constant added or subtracted, meaning it does not go through the origin.
Since the equation \( y = 70x + 500 \) includes the additional 500 miles (the initial distance traveled), it is a nonproportional situation.
Thus, the correct equation is: \[ y = 70x + 500, \text{ nonproportional} \]