Generating graphical representations is an essential skill for productive student engagement in physics laboratory settings, and is a key component in developing representational competency (RC). As physics lab courses have been reformed to prioritize student engagement in authentic scientific skills and practices, students experience additional freedom to decide what data to include in graphs and what types of graph(s) would allow for appropriate sensemaking towards answering experimental questions. With this, however, there is a dearth of PER literature highlighting the strategies students use while working to generate graphs using their own experimental data. This paper presents a case study analysis of a student group's lab investigation to call attention to how students enact various productive strategies when working towards generating graphical representations in an introductory physics laboratory course. Results of this case study analysis identify three productive strategies students enact when working to generate graphs in lab settings, each of which is related to aspects of representational competency (RC): 1) identifying (potential) covarying quantities; 2) choosing representative data subsets suitable for representation; and 3) iteratively reducing data and generating graphs to assess graph's viability in answering research questions. Our analysis also shows how students frequently refer back to their experimental goals and hypotheses when deciding what strategies to enact to generate graphs.