https://file.aiquickdraw.com/mathbot/file/17297444300973lkf1p0t.jpg

To find the **rate of change** represented by the graph, we can calculate the **slope** of the line using two given points. From the image, the points on the line are:

- \((-4, -6)\)  
- \( (4, -2) \)

### Step 1: Apply the slope formula
The slope \(m\) (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### Step 2: Substitute the values
Using \((x_1, y_1) = (-4, -6)\) and \((x_2, y_2) = (4, -2)\):

\[
m = \frac{-2 - (-6)}{4 - (-4)}
\]

### Step 3: Simplify
\[
m = \frac{-2 + 6}{4 + 4} = \frac{4}{8} = \frac{1}{2}
\]

### Final Answer
The **rate of change** (or slope) of the graph is:

\[
m = \frac{1}{2}
\]

This means that for every 2 units increase in \(x\), \(y\) increases by 1 unit.

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Would you like further details on slope or have any questions?

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Here are five related questions to expand your understanding:
1. What does a negative slope represent in a graph?
2. How do you find the slope if the line is vertical or horizontal?
3. What is the equation of a line with slope \(1/2\) passing through \((4, -2)\)?
4. How can you use the slope-intercept form \(y = mx + b\) for this line?
5. How is the rate of change related to real-world problems, such as speed?

**Tip:** Always check if the line passes through the origin (0,0) to make slope calculations quicker!

Find the rate of change represented in the graph.

Learn how to find the rate of change (or slope) of a line from a graph. This example uses two points (-4, -6) and (4, -2) to demonstrate the slope calculation process using the formula m = (y2 - y1) / (x2 - x1). Ideal for students in Grades 6-8.

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