Question

Galvin and Henry 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 Galvin's money box and the number of months (x):

Number of Months
(x)

Amount Remaining (dollars)
(y)

1

80

2

75

3

70

4

65



The equation shows the relationship between the amount of money, y, remaining in Henry's money box and the number of months, x:

Function 2:
y = −7x + 80

Which statement explains which function shows a greater rate of change?
Function 2 shows a greater rate of change, because Henry spends $7 each month and Galvin spends $5 each month.
Function 2 shows a greater rate of change, because Henry spends $80 each month and Galvin spends $15 each month.
Function 1 shows a greater rate of change, because Galvin spends $15 each month and Henry spends $73 each month.
Function 1 shows a greater rate of change, because Galvin spends $5 each month and Henry spends –$7 each month.

Answer 1

the answer would be:
Function 2 shows a greater rate of change because Henry spends $7 each month and Galvin spends $5 each month.

Hope this helps

Answer 2

The correct option is 1.

Explanation:

If a line passing through two points then the slope of the line is

`m=(y_2-y_1)/(x_2-x_1)`

Choose any two points of function 1:

Let the points are (1,80) and (2,75). The rate of change of function 1 is

`m_1=(75-80)/(2-1)=-5`

It means Galvin spends $5 each month.

Henry's money deifned by the equation

`y=-7x+80` .... (1)

The slope intercept form of a line is

`y=mx+b` ... (2)

From (1) and (2) we get

`m_2=-7`

It means Henry's spends $7 each month.

Function 2 shows a greater rate of change, because Henry spends $7 each month and Galvin spends $5 each month.

Therefore the correct option is 1.