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To determine the equation of the line in slope-intercept form \( y = mx + b \) from the given graph, we need to find the slope \( m \) and the y-intercept \( b \).

### Step-by-Step Solution:

1. **Identify two points on the line:**
   - From the graph, two points on the line are \( (-8, -6) \) and \( (8, 6) \).

2. **Calculate the slope \( m \):**
   - The slope \( m \) is calculated as the change in y divided by the change in x:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1}
     \]
     Using the points \((x_1, y_1) = (-8, -6)\) and \((x_2, y_2) = (8, 6)\):
     \[
     m = \frac{6 - (-6)}{8 - (-8)} = \frac{6 + 6}{8 + 8} = \frac{12}{16} = \frac{3}{4}
     \]

3. **Determine the y-intercept \( b \):**
   - The y-intercept \( b \) is where the line crosses the y-axis. From the graph, it's clear that the line crosses the y-axis at \( y = 0 \).

4. **Write the equation in slope-intercept form:**
   - With \( m = \frac{3}{4} \) and \( b = 0 \), the equation of the line is:
     \[
     y = \frac{3}{4}x
     \]

Therefore, the equation of the line in slope-intercept form is:
\[
y = \frac{3}{4}x
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you find the equation of a line given two points?
2. What is the significance of the slope in the equation of a line?
3. How can you determine the y-intercept from a graph?
4. What are the different forms of a linear equation and how do you convert between them?
5. How does changing the slope and y-intercept affect the graph of a line?

### Tip:
Always verify the points you choose for calculating the slope to ensure accuracy in determining the equation of the line.

Write the equation of this line in slope-intercept form.

Learn how to write the equation of a line in slope-intercept form using a graph. This tutorial covers finding the slope and y-intercept from the graph, calculating the slope using two points, and forming the linear equation. Suitable for students in Grades 7-9.

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