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To find the slope of the line passing through the points \((-5, 1)\) and \((5, 6)\), we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

Substitute the given points \((-5, 1)\) and \((5, 6)\) into the formula:

\[
m = \frac{6 - 1}{5 - (-5)} = \frac{5}{5 + 5} = \frac{5}{10} = \frac{1}{2}
\]

So, the slope of the line is \(\frac{1}{2}\).

Now, regarding whether the line rises, falls, is horizontal, or is vertical:

- Since the slope is positive (\(\frac{1}{2}\)), the line rises from left to right.

### Answers:
1. **The slope is \(\frac{1}{2}\).**
2. The line **rises from left to right**.

Let me know if you'd like further details or have any questions!

Here are 5 related questions you might find interesting:
1. How do you find the slope of a vertical line?
2. What does a slope of zero indicate about the line's orientation?
3. Can the slope of a line be a negative number? If so, what does it mean?
4. How do you calculate the slope between points in three-dimensional space?
5. What happens to the slope if two points are identical?

**Tip:** When calculating slope, always subtract in the same order for \(y\)-coordinates and \(x\)-coordinates to avoid sign errors.

Find the slope of the line passing through the points (-5, 1) and (5, 6) or state that the slope is undefined. Indicate whether the line through the points rises, falls, is horizontal, or is vertical.

Learn how to find the slope of a line between the points (-5, 1) and (5, 6). This solution explains the slope formula and how to determine if the line rises or falls. Ideal for students in Grades 7-10 studying coordinate geometry.

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