https://file.aiquickdraw.com/mathbot/file/1725041273645dpp7ysex.jpg

To solve this problem, let's first analyze the given image and identify the question and answer choices.

### Analysis of the Image

The question in the image asks, **"Which equation represents the dotted line?"** There are four answer choices provided:

- **A) \( y = \frac{2}{3}x - 4 \)**
- **B) \( y = -\frac{2}{3}x - 4 \)**
- **C) \( y = \frac{3}{2}x - 4 \)**
- **D) \( y = -\frac{3}{2}x - 4 \)**

The graph shows a line that appears to cross the y-axis at -4 and has a negative slope.

### Determine the Correct Equation

1. **Identify the y-intercept (b):** The line crosses the y-axis at \(-4\). So, the y-intercept \(b = -4\).

2. **Determine the slope (m):** The line has a negative slope. To find the slope, we can use the rise-over-run method:

   - The line goes down 3 units vertically (rise = -3) and goes right 2 units horizontally (run = 2).
   - Slope, \(m = \frac{\text{rise}}{\text{run}} = \frac{-3}{2} = -\frac{3}{2}\).

3. **Form the equation:** Now, using the slope-intercept form of the line equation, \(y = mx + b\), and substituting the slope \(-\frac{3}{2}\) and y-intercept \(-4\), the equation of the line is:

   \[
   y = -\frac{3}{2}x - 4
   \]

### Conclusion

The correct answer is **D) \( y = -\frac{3}{2}x - 4 \)**.

Would you like more details on this solution, or do you have any other questions?

Here are 5 related questions that might interest you:

1. How do you find the slope of a line from two given points?
2. What are the differences between positive and negative slopes?
3. How can you determine if a point lies on a given line?
4. What is the standard form of a linear equation, and how does it differ from the slope-intercept form?
5. How do you convert an equation from slope-intercept form to standard form?

**Tip:** Always identify the y-intercept and slope from the graph first, as they are crucial for determining the correct equation.

Learn how to identify the equation of a line from graph analysis, focusing on the slope-intercept form. This problem covers linear equations and graph interpretation. Suitable for students in Grades 7-9.

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