Question

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

A. The initial value is 2/3, and the rate of change is −2/3.
B. The initial value is -2 and the rate of change is 23.
C. The initial value is −2/3, and the rate of change is 2/3.
D. The initial value is 1/6, and the rate of change is 3/2.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the initial value and rate of change of the linear function, we can use the formula for the slope of a line:

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

Using the points (-4,-10/3) and (-1,-4/3), we can calculate the slope:
slope = ((-4/3) - (-10/3)) / (-1 - (-4))
slope = (6/3) / 3
slope = 2/3

Since the slope represents the rate of change, the rate of change of the linear function is 2/3.

Next, we can use the slope-intercept form of the equation of a line (y = mx + b) to find the initial value (y-intercept). Using the point (-4,-10/3) and the slope of 2/3:

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

Therefore, the initial value of the linear function is -2/3.

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