Question

The table represents a bicycle rental cost in dollars as a function of time in hours.

A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.
Which explains whether or not the function represents a direct variation?

This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.
This function does not represent a direct variation because it does not represent the cost for 1 hour.
This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

Answer 1

The first statement is correct.

The cost is proportional to time: from the table 10 dollars for 2 hours gives a unit rate 10/2 = $5 per hour, so C = 5t. It passes through the origin (0,0) and has constant slope 5, so it is a direct variation.