Determine the initial value and the rate of change of the linear function as given in the graph.
(-1.5,-3), (0,0), (0.5,1)
A. The initial value is -6, and the rate of change is 2
B. The initial value is 0, and the rate of change is 1/2
C. The initial value is 2, and the rate of change is 2.
D. The initial value is 0, and the rate of change is 2
To determine the initial value and the rate of change of a linear function, we need to find the equation of the line that passes through two points on the graph.
The slope or rate of change is equal to the change in y divided by the change in x.
Rate of change = (change in y) / (change in x)
Using the given points (0,0) and (0.5,1), we can calculate the rate of change:
Rate of change = (1 - 0) / (0.5 - 0) = 1 / 0.5 = 2
So, the rate of change is 2.
To find the initial value, we can substitute the coordinates of one of the points into the equation of the line, using the slope-intercept form: y = mx + b, where m is the rate of change and b is the initial value.
Using the point (0,0):
0 = 2(0) + b
0 = 0 + b
b = 0
Therefore, the initial value is 0.
The correct answer is:
D. The initial value is 0, and the rate of change is 2.