https://file.aiquickdraw.com/mathbot/file/1732038285535ijrut59u.jpg

The graph depicts a straight line passing through various points. To analyze and interpret the line, we need to determine key characteristics such as:

1. **Slope (m)**: By observing the rise (change in y) over the run (change in x) between two points.
2. **Y-intercept (b)**: The point where the line crosses the y-axis.
3. **Equation**: Using the form \( y = mx + b \).

From the image, some visible points on the line include:
- \( (-6, 0) \)
- \( (0, 4) \)
- \( (4, 8) \)

### Step-by-Step Analysis:
1. **Calculate the slope \( m \):**
   Using two points, \( (x_1, y_1) = (0, 4) \) and \( (x_2, y_2) = (4, 8) \):
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 4}{4 - 0} = \frac{4}{4} = 1
   \]

2. **Find the y-intercept \( b \):**
   The line crosses the y-axis at \( (0, 4) \), so \( b = 4 \).

3. **Form the equation of the line:**
   Substituting \( m = 1 \) and \( b = 4 \) into \( y = mx + b \):
   \[
   y = x + 4
   \]

### Final Equation:
\[
y = x + 4
\]

Would you like a detailed graph of this line or more analysis?

### Related Questions:
1. How do you calculate the slope using different pairs of points?
2. What is the significance of the y-intercept in the equation of a line?
3. How can you verify the equation of a line using multiple points?
4. What happens to the equation of the line if the slope changes?
5. How can this equation be applied to solve real-world problems?

### Tip:
When identifying the slope, always confirm the direction of the line (increasing or decreasing) to avoid sign errors.

What is the equation of the line shown in the graph?

Learn how to determine the equation of a straight line using the slope and y-intercept. Analyze points from a graph and derive the linear equation y = x + 4 with step-by-step calculations. Suitable for Grades 8-10.

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