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.


The graph represents the direct variation function between earnings in dollars and hours worked.

A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)
Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?

E = 1.5h
E = 7.5h
E = 13h
E = 15h

Answer 1

1) The first choice is correct: This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour (10/2 = 20/4 = 30/6 = 40/8 = 5).

2) E = 7.5h. The slope is 30/4 = 7.5, so E = 7.5·h.