Question

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

the chart has numbers in order (-3,4) (0,3) (3,2) and (6,1)

Answer 2

To determine the initial value and the rate of change of a linear function from a graph, we follow these steps:

1. **Initial Value**: This is the value of the function at the y-intercept, which occurs where the graph intersects the y-axis (x = 0). You will typically read this directly from the graph.

2. **Rate of Change (Slope)**: The rate of change is represented by the slope of the line. To calculate the slope, you can take two points on the line, say (x1, y1) and (x2, y2), and use the formula:

\[
\text{slope} = \frac{y2 - y1}{x2 - x1}
\]

3. **Rounding**: Ensure to round the numeric values to three decimal places as needed.

Since I don't have access to the graph you're referring to, please provide specific points or values from the graph, or describe the graph itself so I can help you determine the initial value and the rate of change.

Answer 3

Thank you for providing the points from the graph. Let's analyze the given points:

- (-3, 4)
- (0, 3)
- (3, 2)
- (6, 1)

### 1. Initial Value:
The initial value (y-intercept) corresponds to the point where \( x = 0 \). From the points you provided, when \( x = 0 \), \( y = 3 \).

**Initial Value:**
\[
3
\]

### 2. Rate of Change (Slope):
To find the rate of change (slope) of the linear function, we can use any two points from the data. Here, let's use the points (0, 3) and (6, 1) for simplicity:

Using the slope formula:
\[
\text{slope} = \frac{y2 - y1}{x2 - x1}
\]

Taking points (0, 3) as \((x1, y1)\) and (6, 1) as \((x2, y2)\):
\[
\text{slope} = \frac{1 - 3}{6 - 0} = \frac{-2}{6} = -\frac{1}{3}
\]

**Rate of Change:**
\[
-\frac{1}{3}
\]

### Summary:
- **Initial Value:** \(3\)
- **Rate of Change:** \(-0.333\) (rounded to three decimal places)

Feel free to ask if you have any more questions or need further assistance!