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To find a vector \( \mathbf{V} \) that moves points along the line \( L \), which passes through the points \( (-8, -1) \) and \( (2, -12) \), we can use the difference between these two points.

1. Let the two points be:
   \[
   P_1 = (-8, -1) \quad \text{and} \quad P_2 = (2, -12)
   \]

2. The vector \( \mathbf{V} \) that moves points along \( L \) can be obtained by subtracting the coordinates of \( P_1 \) from \( P_2 \):
   \[
   \mathbf{V} = P_2 - P_1 = (2 - (-8), -12 - (-1))
   \]

3. Simplifying the components:
   \[
   \mathbf{V} = (2 + 8, -12 + 1) = (10, -11)
   \]

Therefore, the vector \( \mathbf{V} = (10, -11) \) moves points along the line \( L \).

Would you like more details or have any questions?

Here are some related questions you might explore:

1. How would you find the slope of line \( L \) using points \( (-8, -1) \) and \( (2, -12) \)?
2. What is the equation of line \( L \) in slope-intercept form?
3. How can you determine if another point lies on the line \( L \) defined by \( (-8, -1) \) and \( (2, -12) \)?
4. How can you use vector \( \mathbf{V} \) to write a parametric equation for line \( L \)?
5. If \( L \) were extended indefinitely, how could you represent its direction with a unit vector?

**Tip:** When finding a vector along a line passing through two points, subtract the coordinates of the initial point from the terminal point to obtain the direction vector.

The line L passes through the points (-8, -1) and (2, -12). Identify a vector V that moves points along L.

Explore how to find a vector that moves points along a line passing through two points (-8, -1) and (2, -12). This solution covers vector subtraction and coordinate geometry, ideal for students in Grades 10-12.

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