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!