Understanding the concept of straight-line equations is essential as a prerequisite for advanced mathematics. Observations at SMP Negeri 5 Jayapura indicated that eighth-grade students still encountered difficulties, particularly in determining the gradients of parallel and perpendicular lines. This study aimed to describe students' conceptual understanding profiles of straight-line equations based on APOS Theory (Action, Process, Object, and Schema) across high-, medium-, and low-ability categories. The research employed a descriptive qualitative method. Subjects were purposively selected from 27 students based on their MID scores, categorized as high (≥90), medium (80–89), and low (<80), with one student representing each category. The instruments consisted of two essay-type test questions incorporating Papuan cultural contexts and a semi-structured interview guide. The findings revealed that the high-ability student achieved all four APOS stages, the medium-ability student achieved the Action, Process, and Object stages, whereas the low-ability student achieved only the Action stage. Although performance across the Action to Object stages varied, the collective failure of all three subjects in graphical representation indicated cognitive obstacles during the encapsulation process at the Schema stage. These findings recommend the implementation of the APOS-based ACE cycle and special attention to graphical aspects in learning straight-line equations.
