Question

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.

Answer 1

To determine the initial value and the rate of change of the linear function, we need to find the slope of the line passing through the two points:

Slope (rate of change) = (y2 - y1)/(x2 - x1)

For the points (-1.5,-3) and (0,0):
Slope = (0 - (-3))/(0 - (-1.5))
Slope = 3/1.5
Slope = 2

The slope (rate of change) is 2.

Now, let's use one of the given points to find the initial value. We can use the point (0,0):

y = mx + b
0 = 2(0) + b
0 = b

The initial value (y-intercept) is 0.

Therefore, the initial value is 0, and the rate of change is 2.

So, the correct option is:
D. The initial value is 0, and the rate of change is 1/2.