Answer:
<em>First option</em> is the correct answer. i.e. <em>Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.</em>
Step-by-step explanation:
<em>Given:</em>
A little research search shows that you have missed to mention the function 1. So, I am assuming the function 1 was as follows:
<u><em>Function 1
</em></u>
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)
<u><em>Function 2</em></u>
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
<em>Solution:</em>
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, <em>First option</em> is the correct answer. i.e. <em>Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.</em>
Keywords: rate of change, function
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