write an equation involving absolute value for the graph. -5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Recall absolute - value equation form

The general form of an absolute - value equation for a vertical distance between two points on the number line is (|x - a|=b), where (a) is the mid - point between the two points and (b) is the distance from the mid - point to either of the points.

Step2: Find the mid - point

The two points on the number line are (x=-2) and (x = 4). The mid - point (a) between (x_1=-2) and (x_2 = 4) is calculated as (a=\frac{-2 + 4}{2}=\frac{2}{2}=1).

Step3: Find the distance from mid - point

The distance (b) from the mid - point (a = 1) to either (x=-2) or (x = 4) is (|4 - 1|=3) (or (|1-(-2)| = 3)).

Step4: Write the absolute - value equation

The absolute - value equation is (|x - 1|=3).

Answer:

(|x - 1|=3)