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 (a)

The two points on the number line are 5 and 7. The midpoint \( a \) is calculated as \( \frac{5 + 7}{2} = 6 \).

Step2: Find the distance (b) from midpoint to either point

The distance from 6 to 5 (or 7) is \( |6 - 5| = 1 \) (or \( |7 - 6| = 1 \)). So \( b = 1 \).

Step3: Write the absolute value equation

Using the form \( |x - a| = b \), substitute \( a = 6 \) and \( b = 1 \) to get \( |x - 6| = 1 \).

Answer:

\(|x - 6| = 1\)