Let's analyze the number line in the image and answer the questions based on the points provided:

1. Identifying the points:
   The two points on the number line are marked at -2 and 4.

2. Midpoint formula:
   The formula for the midpoint between two points $x_1$ and $x_2$ on a number line is:
   $\text{Midpoint} = \frac{x_1 + x_2}{2}$ Substituting the values: $\text{Midpoint} = \frac{-2 + 4}{2} = \frac{2}{2} = 1$ So, the midpoint is 1.

3. Distance between either point and the midpoint:
   The distance formula between two points on a number line is the absolute difference:
   $\text{Distance} = |x_1 - x_2|$ The distance between -2 and the midpoint (1) is: $|1 - (-2)| = |1 + 2| = 3$ The distance between 4 and the midpoint (1) is: $|4 - 1| = 3$ So, the distance between either point and the midpoint is 3.

4. Absolute value equation:
   The general form of an absolute value equation representing the distance from a point $x$ to a center is: $|x - \text{Midpoint}| = \text{Distance}$ Here, the midpoint is 1, and the distance is 3. Thus, the equation becomes: $|x - 1| = 3$

Answers:

• The midpoint between the two points is 1.
• The distance between either point and the midpoint is 3.
• The absolute value equation for the graph is |x - 1| = 3.

Would you like more details on any of these calculations?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the distance between any two points on a number line?
2. What would the midpoint be if the points were -3 and 5?
3. How does the absolute value equation represent distances on a number line?
4. If one point is shifted further on the number line, how would the equation change?
5. How can the midpoint formula be extended to two-dimensional points?

Tip: The midpoint is always the average of the two numbers, and it's exactly halfway between them.