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.