Answer:
Table c
Step-by-step explanation:
Required:
Which of the 4 has the greatest rate of change
For Graph (A):
We start by picking any two equivalent points on the table:
[tex](x_1,y_1) = (0,1)[/tex]
[tex](x_2,y_2) = (2,5)[/tex]
Next, we determine the slope, m:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5-1}{2-0}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
This represents the rate of change:
For (B): [tex]y = 3x + 7[/tex]
An equation is of the form:
[tex]y = mx + b[/tex]
Where
m represents slope or rate of change:
By comparison:
[tex]m = 3[/tex]
For table (C):
We start by picking any two equivalent points on the table:
[tex](x_1,y_1) = (1,7)[/tex]
[tex](x_2,y_2) = (2,12)[/tex]
Next, we determine the slope, m:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{12-7}{2-1}[/tex]
[tex]m = \frac{5}{1}[/tex]
[tex]m = 5[/tex]
This represents the rate of change:
For (D):
The $1.00 paid every week represents the rate of change.
So:
[tex]m = 1[/tex]
For A - D:
The rate of change are:
[tex]A = 2[/tex]
[tex]B = 3[/tex]
[tex]C = 5[/tex]
[tex]D = 1[/tex]
5 is the greatest.
Hence, (c) has the greatest rate of change
