To determine the initial value and rate of change of the linear function, we need to find the equation of the line passing through the two given points (2.5, 5) and (3.5, 5).
The formula for the equation of a linear function is y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).
Using the formula, we can find the slope (rate of change):
m = (y2 - y1) / (x2 - x1)
m = (5 - 5) / (3.5 - 2.5)
m = 0 / 1
m = 0
Since the slope (rate of change) is 0, the options that have a rate of change of 2 are not correct.
Now let's find the initial value (y-intercept) by substituting one of the given points into the equation:
Using the point (0.5, 1):
1 = 0(0.5) + b
1 = b
Therefore, the initial value (y-intercept) is 1.
The correct answer is:
C: The initial value is 0 and the rate of change is 2.