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 2.5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.

Determine the initial value and the rate of change of the linear function as given in the graph.

(1 point)
The initial value is
, and the rate of change is
.
Remaining Attempts : 3
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Answer 1

To determine the initial value and the rate of change of the linear function depicted in the graph, we can analyze the points through which the line passes.

Given Points:

1. \((-3, 2.5)\)
2. \((0, 1)\)
3. \((2, 0)\)

Initial Value:

The initial value is the y-intercept of the function, which occurs when \(x = 0\). From the given points, at \(x = 0\), the corresponding \(y\)-value is \(1\).

Rate of Change:

The rate of change (slope) can be calculated using the formula: \[ \text{slope} = \frac{\Delta y}{\Delta x} \] To calculate the slope, we can use any two points. Let's use the points \((0, 1)\) and \((2, 0)\).

\[ \Delta y = 0 - 1 = -1 \] \[ \Delta x = 2 - 0 = 2 \] Now, calculating the slope: \[ \text{slope} = \frac{-1}{2} = -0.5 \]

Summary:

• The initial value (y-intercept) is \(1\).
• The rate of change (slope) is \(-0.5\).

Thus, the answer is: The initial value is 1, and the rate of change is -0.5.