write an absolute value equation that represents the graph shown. your answer should use the form |x - a| =…

Explanation:

Step1: Find the mid - point

The two points on the number - line are $x=-8$ and $x = - 1$. The mid - point $a$ between two numbers $x_1$ and $x_2$ is given by $a=\frac{x_1 + x_2}{2}$. So, $a=\frac{-8+( - 1)}{2}=\frac{-8 - 1}{2}=\frac{-9}{2}=-4.5$.

Step2: Find the distance

The distance $b$ from the mid - point to either of the points. Using the point $x=-1$, $b=\vert-1-(-4.5)\vert=\vert-1 + 4.5\vert=\vert3.5\vert = 3.5$.

Step3: Write the absolute - value equation

The absolute - value equation of the form $\vert x - a\vert=b$ is $\vert x+4.5\vert = 3.5$.

Answer:

$\vert x + 4.5\vert=3.5$