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.
rate of change is m =
the initial value is b =

Answer 1

To determine the rate of change, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points from the table.

Using the first two points (2, 22) and (8, 25), we have:
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5

So, the rate of change is 0.5.

To determine the initial value, we can use the formula y = mx + b and substitute one of the points from the table.

Using the first point (2, 22), we have:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21

So, the initial value is 21.

Therefore, the linear function can be written as y = 0.5x + 21.