Data visualizations are an essential tool to comprehend large datasets. However, for visually impaired people (VIP), it is nearly impossible to access visually complex data representations. Current accessibility solutions fall short in providing comprehensive access to data visualizations, which may deter VIPs from pursuing STEM, finance, and other data-heavy fields. We designed and evaluated Sonify - a sonification tool to make data visualizations accessible to VIPs through audio and tactile interactions. This paper is a case study of the iterative design cycle followed while developing Sonify, and the qualitative evaluation of interactions with (n=8) users with visual limitations. We outline the unique challenges of designing for accessibility. We describe creating usability studies to evaluate a sound and touch based interface. Finally, through Sonify, we demonstrate how a novel scrubbing interaction technique makes 2-variable linear graphs accessible to a broader range of people, including those with visual limitations.