Q33. - Algebra 1

Question

Write an equation involving absolute value for each graph.

Step-by-Step Solution

Answer

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

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 -4 and 4.

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

$\begin{array}{c}\text{Midpoint}=\frac{-4+4}{2}\\ =\frac{0}{2}\\ =0\end{array}$

Step-3. Write the equation.

Since, the midpoint of $-4$ and $4$ is $0$, that is, the distance from $-4$ to $0$ is $4$ units and the distance from $0$ to $4$ is also $4$ units.

So, the absolute value equation will be:

$\begin{array}{c}\left|x-0\right|=4\\ \left|x\right|=4\end{array}$