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

Explanation:

Step1: Find the mid - point

The two points on the number line are $x=-9$ and $x = - 3$. The mid - point $a$ between two numbers $x_1$ and $x_2$ is given by $a=\frac{x_1 + x_2}{2}$. So, $a=\frac{-9+( - 3)}{2}=\frac{-9 - 3}{2}=\frac{-12}{2}=-6$.

Step2: Find the distance

The distance $b$ from the mid - point to either of the points is $|-6-( - 9)|=|-6 + 9| = 3$ or $|-3-( - 6)|=|-3 + 6|=3$.

Step3: Write the absolute - value equation

The absolute - value equation of the form $|x - a|=b$ that represents the given graph is $|x+6| = 3$.

Answer:

$|x + 6|=3$