Question

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

Answer 1

Option 3 is the best possible choice

Answer 2

Answer:

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

Step-by-step 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 : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$  ---A

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

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

Substitute the values in A

$y-75=\frac{60-75}{2-1}(x-1)$  

$y-75=-15(x-1)$  

$y=-15x-15+75$  

$y=-15x+60$  

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.