Students often struggle to interpret graphs correctly, despite emphasis on graphic literacy in U.S. education standards documents. The purpose of this study was to describe challenges sixth graders with varying levels of science and mathematics achievement encounter when transitioning from interpreting graphs having discrete independent variables to graphs having continuous independent variables. Data included think-aloud interviews and written line graph interactions. Data analysis focused on three constituent processes of graph interpretation: (1) encoding salient structures, (2) relating salient structures to each other, and (3) understanding referents in relation to salient structures. Difficulties encoding individual data points influenced interpretations of referents and relationships among data points. Cognitive resources learned for interpreting graphs with discrete independent variables both supported and hindered interpretations of graphs with continuous independent variables. Struggles relating graphs to referents reflected inexperience with data collection and analysis. Recommendations are provided to support students during this transition and to improve their ability to answer different types of graph questions.