To find the correct equation relating distance traveled (y) to the hours driven (z) after they have already traveled 500 miles, we can break it down as follows:
They have already traveled 500 miles, and from the next day, their speed is 70 miles per hour. Therefore, the distance they will travel from that point can be expressed as a function of time (in hours).
If \( z \) represents the hours they drive after the first day, the distance they travel on the second day can be given by \( 70z \).
The total distance traveled, \( y \), combines the initial 500 miles and the distance traveled on the second day, which gives us the equation:
\[ y = 70z + 500 \]
This indicates that as they drive more hours at a speed of 70 mph, the total distance increases, starting from 500 miles.
Now we need to determine if this is a proportional or nonproportional situation.
A proportional relationship would imply a direct variation with zero as the starting point, where the equation takes the form \( y = kx \) (where \( k \) is a constant). Since our equation starts at 500 miles and not at 0 (there's a fixed distance already traveled), this indicates a nonproportional situation.
Therefore, the correct equation and classification would be:
y = 70z + 500 nonproportional