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To approximate the slope of the curve at the points marked \((x, y)\) in the graphs, we need to examine the tangent lines drawn at those points. The slope of the tangent line at a particular point on a curve gives us the derivative or the rate of change of the function at that point.

### 1. Graph 1:
- The curve is concave down, and the tangent line is horizontal at the point \((x, y)\). 
- A horizontal line has a slope of **0**. Therefore, the slope of the curve at \((x, y)\) is approximately **0**.

### 2. Graph 2:
- The curve is concave up, and the tangent line has a positive slope at the point \((x, y)\).
- Estimating the rise-over-run, it appears that for every 1 unit moved right on the x-axis, the line rises by about 1 unit. Thus, the slope of the tangent line (and hence the slope of the curve at \((x, y)\)) is approximately **1**.

These approximations are based on the visual observation of the tangent lines in the given graphs.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How do you calculate the slope of a line given two points?
2. What does the slope of a tangent line tell you about the behavior of a function at a point?
3. How is the derivative of a function related to the slope of the tangent line?
4. What does a zero slope indicate about the curve at a particular point?
5. How can you use limits to precisely calculate the slope of a curve?

**Tip**: When approximating slopes from a graph, it's helpful to identify two clear points on the tangent line to use the rise-over-run formula.

Use the figure to approximate the slope of the curve at the point (x, y).

Learn how to approximate the slope of a curve at a given point using the tangent line in the graph. This involves calculating the slope visually and applying concepts of derivatives. Suitable for students in Grades 10-12 studying calculus.

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