Nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his starting point. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. What is one way for Nate to determine the initial value?

Question

By repeatedly adding 50.
By repeatedly subtracting 50.
By repeatedly multiplying by 50.
By repeatedly dividing by 50.

Answer 1

To determine the initial value from a linear function where the rate of change is 50 miles per hour, Nate should use the first value of his table, which corresponds to the distance when the time traveled is zero.

In this context, since the distance changes by 50 miles for each hour traveled, to find the initial value (the distance at the starting point, which is at time = 0), he needs to think backwards from any given distance when time has already passed.

Thus, the correct approach is:

By repeatedly subtracting 50.

This is because, to find the distance at time zero, Nate would subtract 50 miles for each hour that has passed from the distance recorded at that point in time.