To find the midpoint $LM$ between two points on a number line, you can use the midpoint formula. If the two points are $-8$ and $-2$, the midpoint $LM$ can be found as follows:

Step-by-Step Solution:

1. Identify the two points:
   The points given are $-8$ and $-2$.

2. Use the midpoint formula:
   The formula to find the midpoint $M$ between two points $a$ and $b$ on a number line is: $M = \frac{a + b}{2}$

3. Plug in the values:
   Substitute $a = -8$ and $b = -2$ into the formula: $M = \frac{-8 + (-2)}{2}$

4. Simplify the expression: $M = \frac{-8 - 2}{2} = \frac{-10}{2} = -5$

Result:

The midpoint $LM$ on the number line between $-8$ and $-2$ is $-5$.

Would you like more details or have any questions?

Here are 5 related questions to explore this topic further:

1. How do you find the midpoint between two positive numbers on a number line?
2. What is the distance between two points on a number line?
3. How does finding the midpoint change if the two points are the same?
4. Can the midpoint formula be used for coordinates in two-dimensional space? If so, how?
5. How do you find the average of multiple numbers on a number line?

Tip: The midpoint formula is useful in various branches of mathematics, including geometry and algebra, as it helps to find the center point between two numbers or points.