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
To determine the rate of change and the initial value of the linear function, we can use the formula for calculating the slope of a line:
slope = (change in y)/(change in x)
From the table, we can see that the change in x is 8 - 2 = 6, and the change in y is 25 - 22 = 3.
Plugging these values into the formula:
slope = (3)/(6) = 1/2
Therefore, the rate of change of the linear function is 1/2.
To find the initial value (the y-intercept), we can substitute one of the given points into the slope-intercept form of a line:
y = mx + b
Using the point (2, 22):
22 = (1/2)(2) + b
22 = 1 + b
b = 22 - 1
b = 21
So, the initial value of the linear function is 21.