https://file.aiquickdraw.com/mathbot/file/1726889037956gghdx9aw.jpg

The given problem asks to find the rate of change (slope) and the initial value (y-intercept) for a linear function based on the provided graph.

### Step 1: Rate of Change
The rate of change (slope) is provided in the question as \( -\frac{6}{7} \). This means that for every 7 units the line moves horizontally (right), it moves down by 6 units vertically.

### Step 2: Initial Value (y-intercept)
To find the initial value, we need to identify the point where the line intersects the y-axis (where \( x = 0 \)) on the graph. From the graph, it appears that the line crosses the y-axis at \( y = 9 \).

### Answer Summary:
- **Rate of Change (slope)**: \( -\frac{6}{7} \)
- **Initial Value (y-intercept)**: \( 9 \)

Let me know if you'd like more details or explanations!

Here are 5 related questions:
1. What is the equation of the line in slope-intercept form?
2. How do you calculate the slope from two points on a graph?
3. How does the slope affect the direction of the line?
4. What is the significance of the y-intercept in real-world problems?
5. How can you use the slope to predict future values in a linear function?

**Tip**: Always ensure you correctly identify where the line crosses the y-axis to find the initial value!

Find the rate of change and initial value for the linear function from the graph.

Learn how to determine the rate of change and initial value (y-intercept) of a linear function using a graph. This problem explores linear equations, slope-intercept form, and graphical interpretation. Perfect for students in Grades 7-10.

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