Question

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 if change is m = ___, and the initial value is b =____

Answer 1

First, we need to find the rate of change, which is the difference in y divided by the difference in x.

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

So, the rate of change is 0.5.

Next, we need to find the initial value, which is the y-intercept when x = 0. To find the initial value, we can choose one of the points given in the table. Let's use the point (2, 22).

y = m*x + b
22 = 0.5*2 + b
22 = 1 + b
b = 21

So, the initial value is 21.

Therefore, the rate of change is 0.5 and the initial value is 21 for the linear function given by the table.