Question

Write an equation involving absolute value for each graph.

Short answer

The absolute value equation will be $\left|x+3\right|=6$.

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 -9 and 3.

To find the point midway between two points -9 and 3, add the two values and divide by 2.

$\begin{array}{c}\text{Midpoint}=\frac{-9+3}{2}\\ =\frac{-6}{2}\\ =-3\end{array}$

Step-3. Write the equation.

Since, the midpoint of -9 and 3 is -3, that is, the distance from -9 to -3 is 6 units and the distance from -3 to 3 is also 6 units.

So, the absolute value equation will be:

$\begin{array}{c}\left|x-\left(-3\right)\right|=6\\ \left|x+3\right|=6\end{array}$.