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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the initial value and the rate of change of the linear function, we can use two of the provided points on the line. Let's use the points (0, 3) and (3, 2).

The initial value can be found by substituting one of the points into the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the initial value.

Using the point (0, 3):
3 = m(0) + b
b = 3

So, the initial value is b = 3.

Next, we can find the rate of change (slope) using the two points (0, 3) and (3, 2):
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (3 - 0)
m = -1 / 3

So, the rate of change (slope) is -1/3. Rounding to three decimal places, the rate of change is approximately -0.333.