Question

Determine the initial value and the rate of change of the linear function given in the graph.

(-3,2.5)
(0,1)
(2,0)

The initial value is , and the rate of change is .

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the initial value, we need to find the value of the function when x is equal to 0. From the given points, we can see that when x is equal to 0, y is equal to 1. Therefore, the initial value is 1.

To determine the rate of change, we need to calculate the slope of the line connecting two of the given points. Let's use the points (-3, 2.5) and (0, 1) to find the rate of change.

The formula for the slope (rate of change) of a line is given by (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Using the points (-3, 2.5) and (0, 1), we can substitute the values into the formula:

Slope = (1 - 2.5) / (0 - (-3))
= (-1.5) / 3
= -0.5

Therefore, the rate of change is -0.5.