Х 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.
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 need to find the slope of the line passing through the given points.
To find the rate of change (slope), we use the formula:
m = (Y2 - Y1) / (X2 - X1)
Using the points (2,22) and (8,25):
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 0.5
Therefore, the rate of change (slope) is 0.5.
To find the initial value (y-intercept), we can use one of the points and the slope. Let's use the point (2,22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value (y-intercept) is 21.
In conclusion, the rate of change (slope) of the linear function is 0.5 and the initial value (y-intercept) is 21. The linear function can be written as:
Y = 0.5X + 21