Multivariable functions permeate physics, mathematics, and other sciences. Understanding how quantities in multivariable relationships change together – or co-vary – is important for studying physical systems. In this project, we asked junior-level physics majors to describe the covariation of quantities in a multivariable context given a 2D graph. We identified three meta-categories which describe the elements of reasoning students used to make judgements about how quantities covaried: (1) geometric – referencing the features of the provided graph, (2) physical – using physical knowledge about the gas, (3) analytical – analyzing the system abstractly. Students whose problem solving and reasoning fell in the analytical category tended to give the most sophisticated answers. To help students reason productively about covariation in multivariable contexts, we developed an instructional activity where students examine how quantities change using both a 3D surface model and a contour map.