https://file.aiquickdraw.com/mathbot/file/17271074299195975yg80.jpg

To determine which equation matches the given graph, let's analyze the line visually.

### Step 1: Analyze the slope
The line in the image has a **negative slope**, as it is slanting downward from left to right. This tells us that the equation of the line must have a negative coefficient for \( x \) if written in the form \( y = mx + b \).

### Step 2: Analyze the y-intercept
The line crosses the y-axis at a positive point, indicating that the y-intercept \( b \) in the equation \( y = mx + b \) is **positive**.

### Step 3: Check the options
Let's check the given equations and identify which could represent this line:

- **A. \( y = -4x + 2 \)**: This equation has a negative slope (-4) and a positive y-intercept (2), which matches our analysis. So, **Option A** could be correct.
  
- **B. \( 3x + 2y = 6 \)**: Rewriting this equation in slope-intercept form \( y = mx + b \), we solve for \( y \):
  \[
  2y = -3x + 6 \quad \Rightarrow \quad y = -\frac{3}{2}x + 3
  \]
  The slope is negative \(\left( -\frac{3}{2} \right)\), and the y-intercept is 3, so this could also match the graph. **Option B** could be correct.

- **C. \( y = 5 \)**: This represents a horizontal line with slope 0, which does not match the graph. **Option C** is not correct.

- **D. \( 2x - y = 7 \)**: Rewriting this in slope-intercept form:
  \[
  -y = -2x + 7 \quad \Rightarrow \quad y = 2x - 7
  \]
  This equation has a positive slope, so it does not match the graph. **Option D** is not correct.

### Conclusion:
The equations that match the graph are **A** and **B**.

Would you like further details or explanations? Here are 5 follow-up questions:

1. How do we determine the slope from a graph?
2. Why does a negative slope indicate a line slanting downward?
3. What are the general forms of linear equations, and how can we convert between them?
4. How do y-intercepts help in identifying equations?
5. Can you explain how to solve for \( y \) from a standard-form linear equation?

**Tip:** Always check both the slope and y-intercept when matching an equation to a graph.

Which of the following could be the equation of the graph shown below?

Learn how to determine the equation of a line based on the graph provided, focusing on negative slopes and y-intercepts. This problem covers key concepts such as linear equations, graph analysis, and slope-intercept form. Suitable for students in Grades 9-12.

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