Answer:
Function 1 shows a greater rate of change, because Morgan spends $10 each month and Leigh spends $9 each month.
Step-by-step explanation:
The rate of change for function 1 is found using the formula for slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using our points, we have
(40-50)/(2-1) = -10/1 = -10
The rate of change for function 2 is what our variable x is multiplied by; in this case, it is -9.
The rate of change in function 1 is greater because Morgan spends $10 each month while Leigh spends $9 each month.
Answer:
Option A.
Step-by-step explanation:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the rate of change is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given table it is clear that the Function 1 passes through the points (1,50) and (2,40). So, the rate of change of Function 1 is
[tex]m=\frac{40-50}{2-1}[/tex]
[tex]m=\frac{-10}{1}[/tex]
[tex]m=-10[/tex]
Negative sign represents the money spent by Morgan.
The rate of change of Function 1 is -10. It means, Morgan spends $10 each month.
Slope intercept form of a function is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
The Function 2 is
[tex]y=-9x+60[/tex] .... (2)
On comparing (1) and (2) we get
[tex]m=-9, b=60[/tex]
The rate of change of Function 2 is -9. It means, Leigh spends $9 each month.
Function 1 is decreasing at the rate of 10 and Function 2 is decreasing at the rate of 9. So, the Function 1 shows a greater rate of change.
Therefore, the correct option is A.
