https://file.aiquickdraw.com/mathbot/file/1728398364826p4fmmphv.jpg

The graph in the image represents a line, and the question asks which of the given equations Amy wrote. Let's analyze the slope and y-intercept of the line to determine the correct equation.

1. **Slope**: The line appears to be sloping downward, indicating a negative slope. Based on the options, the slope is likely \(-\frac{3}{2}\) since all given equations feature this slope.

2. **Y-intercept**: From the graph, it appears that the line crosses the y-axis at \(y = -1\). This matches the y-intercept in option **A**, which is \(y = -\frac{3}{2}x - 1\).

Thus, the correct equation Amy wrote is **A: \( y = -\frac{3}{2}x - 1 \)**.

Would you like further clarification or additional details?

Here are 5 related questions you might consider:
1. How can we determine the slope of a line from a graph?
2. What is the significance of the y-intercept in a linear equation?
3. How does a negative slope affect the direction of a line on a graph?
4. Can you rewrite the equation in slope-intercept form if given a point and the slope?
5. How can you verify an equation by plugging in points from the graph?

**Tip:** When determining the equation of a line, focus on both the slope (rise over run) and the y-intercept (where the line crosses the y-axis).

This problem involves determining the equation of a line from its graph by analyzing the slope and y-intercept. Suitable for students in Grades 6-8, this solution teaches how to find the correct linear equation in slope-intercept form y = mx + b.

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