Question

The table represents a bicycle rental cost in dollars as a

unction of time in hours.
Bicycle Rental
Time
Cost
(hours)
($)
0
0
2
10
4
20
6
30
8
40
Which explains whether or not the function represents a
direct variation?
O This function represents a direct variation because it
passes through the origin and has a constant rate of
change of $5 per hour.
O This function represents a direct variation because it
has a positive, constant rate of change of $10 per
hour.
O 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

(a) This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

Explanation:

The equation of direct variation is ...

y = kx

for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.

__

constant of variation

Solving the direct variation formula for k, we have ...

k = y/x

Using the table values, we can see if this is constant:

k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5

The "rate of change" is constant at $5 per hour.

The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.