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In this problem, you are asked to find the location of point \( B \) on the number line, such that the ratio of the distances \( \frac{AB}{BC} \) is 1:7. Points \( A \) and \( C \) are already located at \( -1 \) and \( 15 \), respectively.

Let the unknown position of point \( B \) be \( x \).

### Step-by-step solution:

1. **Find the distance between points:**
   - The distance between \( A \) and \( B \) is \( AB = x - (-1) = x + 1 \).
   - The distance between \( B \) and \( C \) is \( BC = 15 - x \).

2. **Set up the ratio:**
   According to the problem, the ratio of \( AB \) to \( BC \) is \( \frac{1}{7} \):
   \[
   \frac{x + 1}{15 - x} = \frac{1}{7}
   \]

3. **Cross-multiply and solve for \( x \):**
   \[
   7(x + 1) = 15 - x
   \]
   Simplifying the equation:
   \[
   7x + 7 = 15 - x
   \]
   Move \( x \) terms to one side:
   \[
   7x + x = 15 - 7
   \]
   \[
   8x = 8
   \]
   Solve for \( x \):
   \[
   x = 1
   \]

Thus, the location of point \( B \) is at \( x = 1 \).

Let me know if you need more details or have any questions!

### Related questions:
1. How would the equation change if the ratio were \( 2:3 \)?
2. What happens if \( B \) is outside the segment \( AC \)?
3. How can we generalize this for any given ratio \( m:n \)?
4. How does the distance formula apply to this situation in higher dimensions?
5. How would this problem change if the points were on a curved path instead of a straight line?

**Tip:** For problems involving ratios on a number line, cross-multiplying after setting up the equation is an efficient method to find the unknown point.

Hallar la ubicación de B de manera que la razón entre AB y BC sea de 1 a 7, dado que A está en -1 y C está en 15.

In this math problem, find the location of point B on a number line such that the ratio between AB and BC is 1:7. Point A is located at -1, and point C is at 15. The solution involves setting up and solving the ratio equation using algebra.

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