Question

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 (slope) and initial value (y-intercept) of the linear function, use the formula:

m = (y2 - y1) / (x2 - x1)

Choose any two points from the table, for example, (2, 22) and (8, 25):

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

The rate of change (slope) is 0.5.

To find the initial value (y-intercept), you can use the point-slope form of the linear equation:

y = mx + b

Using one of the points (2, 22) and the slope we found (m = 0.5):

22 = 0.5*2 + b
22 = 1 + b
b = 21

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