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.
To determine the rate of change, we need to find the difference between the y-values for each pair of corresponding x-values.
For the first pair (2, 22) and second pair (8, 25), the change in y is 25 - 22 = 3.
The change in x is 8 - 2 = 6.
Therefore, the rate of change is 3/6 = 1/2.
To find the initial value, we can choose any pair of x and y values and use the slope-intercept form of a linear equation (y = mx + b) to solve for the initial value (b).
Using the first pair (2, 22), we can substitute these values into the equation:
22 = (1/2)(2) + b
Simplifying, we get:
22 = 1 + b
Subtracting 1 from both sides:
21 = b
Therefore, the initial value (b) of the linear function is 21.
The rate of change is m=
, and the initial value is b=