Question

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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 of the linear function, we can take any of the given points on the line. Let's use the point (0, 3).

The initial value (or y-intercept) is the y-coordinate of this point, which is 3.

To find the rate of change (slope) of the linear function, we can calculate the difference in y-values divided by the difference in x-values between any two points on the line. Let's use the points (0, 3) and (3, 2).

First, calculate the difference in y-values: 2 - 3 = -1
Then, calculate the difference in x-values: 3 - 0 = 3

So, the rate of change (slope) is -1/3.

Therefore, the initial value is 3 and the rate of change is -0.333 (rounded to three decimal places).