Two of the most fundamental skills that students acquire in introductory undergraduate physics laboratory courses are how to accurately plot data and interpret the physical meaning of linear graphs. We redesigned our graphing skills lab with an open-ended approach designed to promote inquiry in graphical analysis and to address specific areas of weakness in students' understanding of graphs. Students had to decide on their own how to graph data in order to promote understanding of linear relationships between variables and slope. Students completing the new open-ended lab developed and retained better graphing skills than students that were taught the lab with a more traditional cookbook approach.