Q46. - Algebra 1

Question

Write an equation involving absolute value for each graph.

Step-by-Step Solution

Answer

The absolute value equation will be $\left|x-0.25\right|=4$.

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 -3.75 and 4.25.

To find the point midway between two points -3.75 and 4.25, add the two values and divide by 2.

$$\begin{gathered} \text{Midpoint}=\frac{-3.75+4.25}{2} \\ =\frac{0.5}{2} \\ =0.25 \end{gathered}$$

Step-3. Write the equation.

Since, the midpoint of -3.75 and 4.25 is 0.25, that is, the distance from -3.75 to 0.25 is 4 units and the distance from 0.25 to 4.25 is also 4 units.

 

So, the absolute value equation will be: $\left|x-0.25\right|=4$.