Q36. - Algebra 1

Question

Write an equation involving absolute value for each graph.

Step-by-Step Solution

Answer

The absolute value equation will be $\left|x+2\right|=4$.

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 2.

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

$\begin{array}{c}\text{Midpoint}=\frac{-6+2}{2}\\ =\frac{-4}{2}\\ =-2\end{array}$

Step-3. Write the equation.

Since, the midpoint of -6 and 2 is -2, that is, the distance from -6 to -2 is 4 units and the distance from -2 to 2 is also 4 units.

 

So, the absolute value equation will be: 

$\begin{array}{c}\left|x-\left(-2\right)\right|=4\\ \left|x+2\right|=4\end{array}$.