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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

The slope formula is:
m = (y2 - y1)/(x2 - x1)

Using the points (-4, -10/3) and (-1, -4/3), we get:
m = ((-4/3) - (-10/3))/((-1) - (-4))
m = (6/3)/(3)
m = 2

The rate of change of the linear function is the slope, which is 2.

Next, we can use one of the given points to find the initial value. We can use the point (-4, -10/3):
y = mx + b
-10/3 = 2(-4) + b
-10/3 = -8 + b
b = 2/3

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