Question

Question

Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 4 right parenthesis, left parenthesis 0 comma 3 right parenthesis, left parenthesis 3 comma 2 right parenthesis, and left parenthesis 6 comma 1 right parenthesis.

Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.

(1 point)
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 can choose any of the given points on the line. Let's choose the point (0, 3).

Therefore, the initial value (y-intercept) of the linear function is 3.

To calculate the rate of change (slope) of the linear function, we can use the formula:

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

Let's use the points (0, 3) and (3, 2) to calculate the slope:

slope = (2 - 3) / (3 - 0) = -1 / 3

Therefore, the rate of change (slope) of the linear function is -1/3.