Question

The table shows the relationship between the amount of money (y) remaining in Maddy's money box and the number of months (x): Function 1 Number of Months (x) Amount Remaining (in dollars) (y) 1 100 2 80 3 60 4 40 The equation shows the relationship between the amount of money (y) remaining in Caitlin's money box and the number of months (x): Function 2: y = −18x + 120 Which statement explains which function shows a greater rate of change? Function 2 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month. Function 2 shows a greater rate of change, because Maddy spends $100 each month and Caitlin spends $120 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends −$18 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

Answer 1

Maddie :
(1,100),(2,80)
slope (rate of change) = (80 - 100) / (2 - 1) = -20/1 = -20

Caitlin :
y = -18x + 120......slope (rate of change) = -18

To determine which rate of change is greater, take the absolute value of the slopes.
 Maddy : | -20 | = 20
Caitlin : | -18 | = 18
 the greater rate of change is the one with the larger absolute value....so that would be Maddy...function 1 shows a greater rate of change because Maddie spends 20 each month and Caitlin spends 18 each month