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Sandra and Jenny 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 Sandra's money box and the number of months (x): Number of Months (x) Amount Remaining (dollars) (y) 1 50 2 45 3 40 4 35 The equation shows the relationship between the amount of money, y, remaining in Jenny's money box and the number of months, x: Function 2: y = −6x + 50 Which statement explains which function shows a greater rate of change? Function 2 shows a greater rate of change because Jenny spends $6 each month and Sandra spends $5 each month. Function 2 shows a greater rate of change because Jenny spends $50 each month and Sandra spends $15 each month. Function 1 shows a greater rate of change because Sandra spends $15 each month and Jenny spends $44 each month. Function 1 shows a greater rate of change because Sandra spends $5 each month and Jenny spends –$6 each month.

Respuesta :

Function 2 shows a greater rate of change because Jenny spends $6 each month and Sandra spends $5 each month. So, the correct option is A) and this can be determined by using the point-slope form of the line.

Given :

  • Sandra and Jenny spend a certain amount of money from their money box each month to buy plants.
  • The table given shows the relationship between the amount of money (y) remaining in Sandra’s money box and the number of months.
  • y = -6x + 50

The equation of function 1 can be determined by using the point-slope form of the line.

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Now, put the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] from the given table in equation (1).

[tex]\dfrac{y-50}{x-1}=\dfrac{45-50}{2-1}[/tex]

[tex]\dfrac{y-50}{x-1}=-5[/tex]

y - 50 = -5x + 5

y + 5x = 55

y = -5x + 55

The magnitude of the slope of function 1 is 5 and the magnitude of the slope of function 2 is 6.

Therefore, function 2 shows a greater rate of change because Jenny spends $6 each month and Sandra spends $5 each month. So, the correct option is A).

For more information, refer to the link given below:

https://brainly.com/question/837699

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