Question

the table shows the relationship between the number of games bowled and the total cost including shoe rental.
total cost including shoe rental
number of games | 1 | 2 | 3 | 4
total cost (in dollars) | 9 | 13 | 17 | 21
choose all the correct statements about the rate of change and initial value of the relationship.
a. the cost of shoe rental is $4.00
b. the cost of shoe rental is $5.00
c. the cost of shoe rental is $9.00
d. the cost per game is $4.00
e. the cost per game is $5.00
f. the cost per game is $9.00

Explanation:

Step1: Find cost per game (rate of change)

Rate of change = $\frac{\text{Change in total cost}}{\text{Change in number of games}} = \frac{13-9}{2-1} = 4$

Step2: Find shoe rental (initial value)

Let initial value = $b$, use $y=mx+b$ (1 game, $y=9$, $m=4$):
$9 = 4(1) + b$
$b = 9 - 4 = 5$

Answer:

B. The cost of shoe rental is $5.00
D. The cost per game is $4.00