Use the table to answer the question
× 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, we can use the formula:
m = (change in y) / (change in x)
First, let's calculate the change in y:
Change in y = 25 - 22 = 3
Next, let's calculate the change in x (which in this case is the difference between the x values):
Change in x = 8 - 2 = 6
Now, we can plug these values into the formula to find the rate of change (m):
m = 3 / 6 = 0.5
So, the rate of change is m = 0.5.
To determine the initial value (y-intercept), we can choose one of the points on the line and plug it into the equation y = mx + b. Let's use the point (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value is b = 21.