To create an equation for the total distance traveled (\(y\)) in relation to the hours driven (\(x\)), we consider that they have already traveled 500 miles and will be adding to that distance based on their travel at an average speed of 70 miles per hour.
We can set up the equation as follows:
\[ y = 70x + 500 \]
In this equation:
- \(y\) represents the total distance traveled,
- \(x\) represents the number of hours driven, and
- the term \(70x\) accounts for the additional distance traveled at 70 miles per hour after they have already traveled 500 miles.
To determine if this situation is proportional or non-proportional:
- A proportional situation would imply that the relationship can be described by the equation \(y = kx\) (i.e., the distance is directly proportional to the hours with no fixed amount added).
- A non-proportional situation involves a constant (a fixed value), which in this case is the initial 500 miles.
Since this equation includes the fixed value of 500 miles, it represents a non-proportional relationship.
Therefore, the correct answer is:
\(y = 70x + 500\), nonproportional.
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