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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the initial value and rate of change of the linear function represented by the given graph, we first need to find the slope of the line using two points on the line. Let's take the points (0, 3) and (3, 2) from the graph:

Slope (m) = (y2 - y1) / (x2 - x1)
Slope = (2 - 3) / (3 - 0)
Slope = -1 / 3

Now that we have the slope, we can determine the initial value (y-intercept) of the function by substituting one of the points into the slope-intercept form of a linear equation (y = mx + b). Let's use the point (0, 3) and the slope we found:

3 = (-1/3)(0) + b
b = 3

Therefore, the linear function can be expressed as y = -1/3x + 3.

The initial value is 3 and the rate of change is -1/3.