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

Answer 1

To determine the rate of change, we can calculate the slope between the two points given in the table.

Slope (m) = (y2 - y1) / (x2 - x1)
= (25 - 22) / (8 - 2)
= 3 / 6
= 0.5

Therefore, the rate of change (slope) of the linear function is m = 0.5.

To determine the initial value, we can use the equation of a line: y = mx + b. We can choose one of the points given in the table to plug in the values and solve for b.

Using the point (2, 22),
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21

Therefore, the initial value of the linear function given in the table is b = 21.