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The problem is asking to find the slope of the line passing through two points and to determine if the line rises, falls, is horizontal, or is vertical.

The two points given are:
\[
\left(\frac{5}{2}, -2\right) \quad \text{and} \quad \left(\frac{5}{2}, \frac{1}{2}\right)
\]

To find the slope \(m\) of the line between these two points, we use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the coordinates:
\[
m = \frac{\frac{1}{2} - (-2)}{\frac{5}{2} - \frac{5}{2}} = \frac{\frac{1}{2} + 2}{0}
\]

The denominator is 0, which means the slope is undefined. This happens when the line is vertical.

So, the correct answer is:
**The line is vertical.**

Would you like further explanation on how to handle undefined slopes?

Here are 5 related questions to explore:
1. How do you find the slope of a line given two points?
2. What does it mean when the slope is zero?
3. How can you recognize a vertical line from an equation or points?
4. What is the difference between undefined slope and zero slope?
5. How do horizontal and vertical lines differ in slope and equation?

**Tip:** When the x-coordinates of two points are the same, the line is always vertical and the slope is undefined.

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then, indicate whether the line through the points rises, falls, is horizontal, or is vertical. Points: (5/2, -2) and (5/2, 1/2).

Learn how to determine the slope of a vertical line passing through points (5/2, -2) and (5/2, 1/2). This problem covers the concept of undefined slopes and how to recognize vertical lines. Suitable for students in Grades 8-10.

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