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.
The rate of change is m= _____, and the initial value is b= _____.
To find the rate of change, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the values from the table:
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 from the table (let's use the point (2, 22)):
22 = 0.5(2) + b
22 = 1 + b
b = 21
So, the initial value is b = 21.