y = −9x + 60

Which statement explains which function shows a greater rate of change?
Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.
Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
Function 2 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $60 each month.
Function 2 shows a greater rate of change, because Morgan spends $50 each month and Leigh spends −$9 each month.

First option is the correct answer. i.e. Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.

Step-by-step explanation:

Given:

A little research search shows that you have missed to mention the function 1. So, I am assuming the function 1 was as follows:

Function 1

This function shows the relationship between the amount (in $) (y) remaining in Morgan's money box and number of months (x).

So, below is the function 1.

1(x) 50(y)

2(x) 40(y)

3(x) 30(y)

4(x) 20(y)

Function 2

The equation shows the relationship between the amount of money (in $) (y) remaining in Leigh’s money box and the number of months (x).

So, below is the function 2.

y = −9x + 60

Solution:

For function 1, we need to use the slop formula to determine the rate of change for function 1, which is given by:

m = (y² - y¹) ÷ (x² - x¹)

Putting the point (x¹, y¹) = (1, 50) and (x², y²) = (2, 40) in slope formula:

m = (y² - y¹) ÷ (x² - x¹)

= (40 - 50) ÷ (2 - 1)

= (-10) ÷ (1)

= ( -10) × (1) = -10

The negative sign indicates that money was spent by Morgan each month. So, the rate of change would be m = -10.

For function 2, we need to use the slop intercept form of equation to determine the rate of change for function 2, which is given by:

y = mx + b

Here, m is represented as slop and b is treated as y-intercept.

As the function is given by:

y = −9x + 60

Here, m = -9 and b = 60

So, the rate of change is -9 for function 2, meaning Leigh is spending $9 each month, and negative sign indicates money is being spent.

Therefore, if we compare the rate of change of function 1 with the rate of change of function 2, we can establish that rate of function 1 shows a greater rate of change, because Morgan spends spends $10 each month and Leigh spends $9 month each month.

Hence, First option is the correct answer. i.e. Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.

Keywords: rate of change, function

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