Question

Lenny and Thad spend a certain amount of money from their money box each month to buy comic books.

The table shows the relationship between the amount of money (y) remaining in Lenny's money box and the number of months (x):

Function 1
Number of Months
(x) Amount Remaining (in dollars)
(y)
1 75
2 60
3 45
4 30


The equation shows the relationship between the amount of money (y) remaining in Thad's money box and the number of months (x):

Function 2:
y = −12x + 80

Which statement explains which function shows a greater rate of change?
Function 2 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.
Function 2 shows a greater rate of change, because Lenny spends $75 each month and Thad spends $12 each month.
Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.
Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $80 each month.

Answer 1

option 3 is the best possible choice

Answer 2

Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.

Explanation:

Function 1:

(x) Amount Remaining (in dollars) (y)

1 75

2 60

3 45

4 30

Now to find the the equation shows the relationship between the amount of money (y) remaining in Thad's money box and the number of months (x) we will use two point slope form

Two point slope form :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)` ---A

`(x_1,y_1)=(1,75)`

`(x_2,y_2)=(2,60)`

Substitute the values in A

`y-75=(60-75)/(2-1)(x-1)`

`y-75=-15(x-1)`

`y=-15x-15+75`

`y=-15x+60`

General equation of line :
`y =mx+c`-- B

Where m is the rate of change

So, Function 1:
`y=-15x+60`

Comparing with B

m = -15

y = remaining amount

x = no. of months

So, In function (1) $15 is spent per month

Function 2:
`y = -12x + 80`

Comparing with B

m = -12

So, In function (2) $12 is spent per month

Thus Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.

Hence Option C is correct.