Question

Ronin and Tom spend a certain amount of money from their money box each month to buy plants. The table shows the relationship between the amount of money (y) remaining in Ronin's money box and the number of months (x): Number of Months (x) Amount Remaining (dollars) (y) 1 70 2 67 3 64 4 61 The equation shows the relationship between the amount of money, y, remaining in Tom's money box and the number of months, x: Function 2: y = −4x + 70 Which statement explains which function shows a greater rate of change? Function 2 shows a greater rate of change, because Tom spends $70 each month and Ronin spends $9 each month. Function 2 shows a greater rate of change, because Tom spends $66 each month and Ronin spends $9 each month. Function 2 shows a greater rate of change, because Tom spends $4 each month and Ronin spends $3 each month. Function 1 shows a greater rate of change, because Ronin spends $3 each month and Tom spends –$4 each month.

Answer 1

Ronin :
(1,70)(2,67)
slope (rate of change) = (67 - 70) / (2 - 1) = -3/1 = -3

Tom :
y = -4x + 70......In y = mx + b form, the slope can be found in the m position. So the slope of this line is -4

Function 2 shows a greater rate of change because Tom spends $4 each month and Ronin spends $ 3 each month

Answer 2

Based on the calculations, function 2 shows a greater rate of change, because Tom spends $4 each month and Ronin spends $3 each month: option C.

What is a slope?

A slope is also referred to as gradient and it's typically used to describe the rate of change between the points of a data set.

How to calculate the rate of change?

Mathematically, the slope (rate of change) can be calculated by using this formula;

Slope = $\frac{Change \ in \ y-axis}{Change \ in \ x-axis}$

Slope  = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

For Ronin's money box, we have:

Points (x, y) = (1, 70) (2, 67)

Slope  = $\frac{67 - 70}{2 - 1}$

Slope = -3

Since Tom's money box is given by this function y = -4x + 70. Thus, the slope is equal to -4.

In order to determine which slope (rate of change) is greater, we would take the absolute value of the slopes as follows:

Ronin = |-3| = 3.

Tom = |-4| = 4.

Therefore, Tom's function shows a greater rate of change because he spends $4 each month while Ronin spends $3 each month.

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