Question

write an absolute value equation that represents the graph shown.
your answer should use the form |x - a| = b or |x + a| = b, where a and b are whole numbers, decimals, or simplified fractions.

Explanation:

Step1: Find the midpoint of the two points

The two points on the number line are -9 and -4. The midpoint (a - value in the absolute value equation) is calculated as the average of the two points. So, midpoint $a = \frac{-9 + (-4)}{2} = \frac{-13}{2} = -6.5$. Wait, but maybe we can think of the absolute value equation $|x - h| = k$, where $h$ is the midpoint and $k$ is the distance from the midpoint to either point.

Step2: Calculate the distance from midpoint to a point

Distance from -6.5 to -9: $|-9 - (-6.5)| = |-2.5| = 2.5$. So the equation should be $|x - (-6.5)| = 2.5$ or $|x + 6.5| = 2.5$. Wait, but let's check again. Wait, the two points are -9 and -4. The midpoint between -9 and -4 is $\frac{-9 + (-4)}{2}=\frac{-13}{2}=-6.5$. The distance from -6.5 to -9 is $|-9 - (-6.5)| = 2.5$, and to -4 is $|-4 - (-6.5)| = 2.5$. So the absolute value equation is $|x + 6.5| = 2.5$ (since $x - (-6.5)=x + 6.5$).

Answer:

$|x + 6.5| = 2.5$