Question

Write an equation involving absolute value for each graph.

Short answer

The absolute value equation will be $\left|x+0.33\right|=1$.

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 -1.5 and 1.5.

To find the point midway between two points -1.33 and 0.67, add the two values and divide by 2.

$\begin{array}{c}\text{Midpoint}=\frac{-1.33+0.67}{2}\\ =\frac{-0.66}{2}\\ =-0.33\end{array}$

Step-3. Write the equation.

Since, the midpoint of -1.33 and 0.67 is -0.33, that is, the distance from -1.33 to -0.33 is 1 unit and the distance from -0.33 to 0.67 is also 1 unit.

So, the absolute value equation will be:

$\begin{array}{c}\left|x-\left(-0.33\right)\right|=1\\ \left|x+0.33\right|=1\end{array}$