To determine the length of segment \( \overline{JK} \), we can use the information given about the lengths of segments \( \overline{IK} \) and \( \overline{IJ} \).
We know:
- The length of segment \( \overline{IK} = 15 \)
- The length of segment \( \overline{IJ} = 13 \)
Since \( J \) is on the line segment \( \overline{IK} \), we can write the following relationship:
\[ \overline{IK} = \overline{IJ} + \overline{JK} \]
Now we can substitute the known lengths into the equation:
\[ 15 = 13 + \overline{JK} \]
To solve for \( \overline{JK} \), we can subtract \( 13 \) from both sides:
\[ \overline{JK} = 15 - 13 \]
Thus:
\[ \overline{JK} = 2 \]
Therefore, the length of segment \( \overline{JK} \) is \( \boxed{2} \).