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To find the equation of the line in slope-intercept form \( y = mx + b \), we need two key components:

1. **The slope (m)**.
2. **The y-intercept (b)**, which is where the line crosses the y-axis.

### Step 1: Determine the slope \(m\)
The slope \(m\) of a line is calculated as the "rise over run" between two points on the line:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph, we can identify two points:
- Point 1: \( (-8, -4) \)
- Point 2: \( (4, 2) \)

Now calculate the slope:
\[
m = \frac{2 - (-4)}{4 - (-8)} = \frac{6}{12} = \frac{1}{2}
\]
So, the slope is \( m = \frac{1}{2} \).

### Step 2: Determine the y-intercept \(b\)
The y-intercept is where the line crosses the y-axis. From the graph, the line crosses the y-axis at \( y = -1 \). Therefore, \( b = -1 \).

### Final Equation
Substitute \(m = \frac{1}{2}\) and \(b = -1\) into the slope-intercept form \(y = mx + b\):
\[
y = \frac{1}{2}x - 1
\]

This is the equation of the line in fully simplified slope-intercept form.

Would you like more details on any part of the solution? 

Here are 5 related questions you can explore:
1. How do you calculate the slope if only one point is given?
2. What is the general formula for converting standard form to slope-intercept form?
3. How does the slope affect the angle or steepness of the line?
4. Can you graph a line if only its equation is provided?
5. How would the equation change if the slope were negative?

**Tip:** When calculating the slope from a graph, always pick points where the line crosses grid intersections to make the calculation easier and more accurate.

Write the equation of the line in fully simplified slope-intercept form based on the graph provided.

This problem involves finding the equation of a line in slope-intercept form using a graph. Key concepts include slope calculation, linear equations, and algebra. Suitable for students in Grades 8-10.

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