Question

Determine the initial value and the rate of change of the linear function as given: (-4,-10/3) (-1,-4/3)

A. The initial value is -2/3, and the rate of change is 2/3.
B. The initial value is 1/6, and the rate of change is 3/2
C. The initial value is -2, and the rate of change is 2/3
D. The initial value is 2/3, and the rate of change is -2/3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the initial value and the rate of change of a linear function, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the rate of change and b is the initial value.

Using the given points (-4,-10/3) and (-1,-4/3), we can find the slope (rate of change):

m = (change in y) / (change in x)

m = (-4/3 - (-10/3)) / (-1 - (-4))
= (-4/3 + 10/3) / (-1 + 4)
= 6/3 / 3
= 2/3

So, the rate of change is 2/3.

Now, we can use one of the points and the rate of change to find the initial value (b). Let's use the point (-4,-10/3):

-10/3 = (2/3)(-4) + b
-10/3 = -8/3 + b
b = -10/3 + 8/3
b = -2/3

Therefore, the initial value is -2/3 and the rate of change is 2/3.

Thus, the answer is A. The initial value is -2/3 and the rate of change is 2/3.