Question

Write an equation involving absolute value for each graph.

Short answer

The absolute value equation will be $\left|x\right|=6$.

Step-by-step solution

Step-1. Define absolute value equation.

For any real numbers a and b, if$\left|a\right|=b$and $b\ge 0$, then$a=b$or $a=-b$.

Step-2. Find the mid-point of points -6 and 6.

To find the point midway between two points -6 and 6, add the two values and divide by 2.

$\begin{array}{c}\text{Midpoint}=\frac{-6+6}{2}\\ =\frac{0}{2}\\ =0\end{array}$

Step-3. Write the equation.

Since, the midpoint of -6 and 6 is 0, that is, the distance from -6 to 0 is 6 units and the distance from 0 to 6 is also 6 units.

So, the absolute value equation will be:

$\begin{array}{c}\left|x-0\right|=6\\ \left|x\right|=6\end{array}$