Use the image to answer the question.

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

To find the initial value and the rate of change (slope) of the linear function depicted in the graph, we can use the information from the given points on the line.

1. Identify two points on the line: Let's take the points (0, 3) and (3, 2) for calculation.

2. Calculate the rate of change (slope) using the formula: \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the chosen points: \[ m = \frac{2 - 3}{3 - 0} = \frac{-1}{3} = -0.333 \]

3. Determine the initial value: The initial value (y-intercept) is the value of \( y \) when \( x = 0 \). From the point (0, 3), we see that the initial value is: \[ \text{Initial Value} = 3 \]

Putting it all together:

• The initial value is 3.
• The rate of change is -0.333 (rounded to three decimal places).

Final result:

• The initial value is 3, and the rate of change is -0.333.