To create an equation involving absolute values for the points $-2$ and $4$, we can use the midpoint of these two numbers to create an absolute value equation that expresses the distance between any point $x$ and the midpoint of the two points. The midpoint between $-2$ and $4$ is:

$\text{Midpoint} = \frac{-2 + 4}{2} = 1$

The absolute value equation expressing the distance between $x$ and the midpoint 1, while covering both points $-2$ and $4$, is:

$|x - 1| = 3$

This equation means that the distance between $x$ and $1$ is always 3 units, which places $x$ at $-2$ or $4$. Therefore, this absolute value equation represents the points $-2$ and $4$ on a number line.

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. How would the equation change if the points were $-5$ and $3$?
2. What would the absolute value equation look like if the graph had only one point, such as $2$?
3. How can you graph this equation on a coordinate plane?
4. What is the general formula for an absolute value equation given two points on a number line?
5. How can this absolute value equation be solved algebraically?

Tip: When dealing with absolute value equations, think of them as representing distances from a certain point.