Use the table to answer the question.
Input
(Boxes) Output
(Cost)
1 2.25
2 4.50
3 6.75
4 9.00
How can this function be represented algebraically?
(1 point)
Responses
y=2.25x
y equals 2.25 x
y=x+2.25
y equals x plus 2.25
y=−2.25x
y equals negative 2.25 x
y=x−2.25
The output cost is directly proportional to the number of boxes, and each box increases the cost by 2.25. So, we can establish a direct relationship where the cost (y) equals 2.25 times the number of boxes (x). The correct algebraic representation of this function, based on the given table, is therefore:
y = 2.25x
The other options do not correctly represent the relationship between the number of boxes and the cost:
- y = x + 2.25 would suggest that there is a fixed cost of 2.25 plus the number of boxes, which is incorrect.
- y = −2.25x would incorrectly indicate that the cost decreases as the number of boxes increases.
- y = x − 2.25 would suggest there is a starting value subtracted by 2.25 for each box, which is also incorrect.
Hence, the first response is the correct one:
y = 2.25x