Use the table to answer the question.

Question

x y
2 22
8 25

Determine the rate of change and the initial value of the linear function given here as a table of values. (1 point)

The rate of change is m=, and the initial value is b=
.

Answer 1

The rate of change can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5

So, the rate of change is m=0.5.

To find the initial value, we can use the point-slope form of a linear equation:

y = mx + b

Using one of the points given (8, 25) and the rate of change we just found (m=0.5):

25 = 0.5(8) + b
25 = 4 + b
b = 21

So, the initial value is b=21.

Answer 2

The rate of change is m= , and the initial value is b=.

Answer 3

The rate of change is m=0.5, and the initial value is b=21.