Determine the initial value and the rate of change of the linear function as given: (-1.5,3) (0,0) (0.5,1)
A. The initial value is 2, and the rate of change is 2.
B. The initial value is 0, and the rate of change is 2.
C. The initial value is -6, and the rate of change is 2.
D. The initial value is 0, and the rate of change is 1/2.
To determine the initial value and rate of change, you can use the formula for the equation of a line: y = mx + b, where m represents the rate of change and b represents the initial value.
Using the given points (-1.5,3), (0,0), and (0.5,1), you can plug in the x and y values to find the equation of the line.
For the first set of points (-1.5,3), you would have 3 = (-1.5)m + b.
For the second set of points (0,0), you would have 0 = 0m + b.
For the third set of points (0.5,1), you would have 1 = (0.5)m + b.
Simplifying the first equation, you get 3 = -1.5m + b.
Since the second equation is 0 = 0m + b, this would imply that b = 0.
Thus, you have the equation 3 = -1.5m + 0.
Simplifying, you get 3 = -1.5m.
Dividing both sides by -1.5, you get -2 = m.
Therefore, the initial value is 0 and the rate of change is -2. However, none of the given answer choices match this result.