Question

The rate of change is m=
, and the initial value is b=
.
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.

Answer 1

To determine the rate of change and the initial value of the linear function, we can use the formula for a linear function: y = mx + b, where m is the rate of change and b is the initial value.

We are given the following data points:
(2, 22) and (8, 25)

First, we can calculate the rate of change (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5

Next, we can substitute one of the data points into the formula y = mx + b to solve for b:
Using the point (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 21

Therefore, the rate of change of the linear function is 0.5 and the initial value is 21.