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=
To determine the rate of change and initial value of the linear function, we can use the formula for slope (rate of change):
m = (y2 - y1) / (x2 - x1)
Using the values from the table:
m = (25 - 22) / (8 - 2)
= 3 / 6
= 1/2
Therefore, the rate of change (m) is 1/2.
To find the initial value (y-intercept, b), we can choose any point from the table and substitute it into the slope-intercept form of a linear equation:
y = mx + b
Let's use the first point (2, 22):
22 = (1/2)(2) + b
22 = 1 + b
b = 22 - 1
= 21
Therefore, the initial value (b) is 21.