Question

Use the table to answer the question. x 2 8 y 22 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= 0.5 and the initial value is b= ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change, we need to calculate the difference in the y-values divided by the difference in the x-values:

Rate of change (m) = (change in y)/(change in x) = (25-22)/(8-2) = 3/6 = 0.5

So, the rate of change of the linear function is 0.5.

To find the initial value (y-intercept or b), we can choose any pair of values from the table and use the slope-intercept form of a linear equation:

y = mx + b

Using the point (2, 22) from the table:

22 = 0.5(2) + b

22 = 1 + b

b = 22 - 1

b = 21

So, the initial value of the linear function is b = 21.