Functions Unit Test

Question

5 of 155 of 15 Items

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=
.
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Answer 1

To determine the rate of change, we need to find the slope of the line passing through the points (2,22) and (8,25).

First, calculate the change in y: 25 - 22 = 3
Next, calculate the change in x: 8 - 2 = 6

Now, we can calculate the rate of change (slope):
m = (change in y)/(change in x) = 3/6 = 0.5

Therefore, the rate of change is m= 0.5.

To find the initial value (y-intercept), we can substitute one of the points into the slope-intercept form of a linear equation, y = mx + b.

Using the point (2,22):

22 = 0.5(2) + b
22 = 1 + b
b = 21

Therefore, the initial value is b= 21.