Question

Write an equation involving absolute value for each graph.

Short answer

The absolute value equation will be $\left|x-0.5\right|=3$.

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 -2.5 and 3.5.

To find the point midway between two points -2.5 and 3.5, add the two values and divide by 2.

$\begin{array}{c}\text{Midpoint}=\frac{-2.5+3.5}{2}\\ =\frac{1}{2}\\ =0.5\end{array}$

Step-3. Write the equation.

Since, the midpoint of -2.5 and 3.5 is 3, that is, the distance from -2.5 to 0.5 is 3 units and the distance from 0.5 to 3.5 is also 3 units.

So, the absolute value equation will be: $\left|x-0.5\right|=3$.