This problem requires finding the missing value in the equation $-5 = -10 + \_\_\_$, using the number line.

Step-by-step solution:

1. Start with the given equation: $-5 = -10 + \_\_$

2. Rearrange to isolate the missing value (__): $\_\_ = -5 - (-10)$

3. Simplify the expression: $\_\_ = -5 + 10$

4. Calculate: $\_\_ = 5$

Final Answer:

The missing value is 5.

The number line helps verify this: starting from $-10$, you need to add $5$ to reach $-5$.

Would you like further clarification or more examples?

Here are five questions to expand on this concept:

1. How can a number line be used to visually solve equations like this?
2. What is the importance of adding and subtracting integers in algebra?
3. How can you rewrite equations to isolate the variable more easily?
4. Can this process work for equations involving fractions or decimals?
5. What other methods besides the number line can confirm the solution?

Tip: Always double-check your calculations when working with negatives, as small errors can lead to incorrect answers!