Question

Write an equation involving absolute value for each graph.

Short answer

The absolute value equation will be $\left|x-1\right|=3$.

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 and 4.

To find the point midway between two points -2 and 4, add the two values and divide by 2.

$\begin{array}{c}\text{Midpoint}=\frac{-2+4}{2}\\ =\frac{2}{2}\\ =1\end{array}$

Step-3. Write the equation.

Since, the midpoint of -2 and 4 is 1, that is, the distance from -2 to 1 is 3 units and the distance from 1 to 4 is also 3 units.

So, the absolute value equation will be:$\left|x-1\right|=3$.