Use the table to answer the 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=
.
To determine the rate of change (m) of a linear function, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the points (2, 22) and (8, 25) from the table to calculate the rate of change:
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5
So, the rate of change is 0.5.
To determine the initial value (b) of the linear function, we can use the formula:
y = mx + b
Using one of the points from the table, for example (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 21
So, the initial value is 21.
Therefore, the rate of change is m=0.5 and the initial value is b=21.