write an equation involving absolute value for the graph.

Explanation:

Step1: Identify the mid - point

The mid - point between the two points on the number line is $\frac{-2 + 4}{2}=1$.

Step2: Calculate the distance from the mid - point

The distance from the mid - point $x = 1$ to either $x=-2$ or $x = 4$ is $|4 - 1|=3$.

Step3: Write the absolute - value equation

The general form of an absolute - value equation for the set of points that are a distance $d$ from a point $a$ is $|x - a|=d$. Here, $a = 1$ and $d = 3$, so the equation is $|x - 1|=3$.

Answer:

$|x - 1|=3$