This study reports on the development, validation, and administration of a 48-item multiple-choice test to assess students' representational fluency of linear functions in a physics context (1D kinematics) and a mathematics context. The test includes three external representations: graphs, tables, and formulas, which result in six possible representational transitions between them. Moreover, four linear function types are included: negative y intercept and positive slope, zero y intercept and positive slope, positive y intercept and negative slope, and positive y intercept and positive slope. The test is administered to 385 students aged 14-15 in the 9th grade from 13 schools in Flanders (Belgium) and-after validation-is analyzed by means of generalized estimating equations (GEE). The results show a significant main effect for all design factors and a significant interaction effect between representational transition and function type, as well as additional interaction effects with the gender of the respondents. Furthermore, representational transitions which include a formula prove to be significantly more difficult; in particular for the directly proportional function type, the transition to a formula stands out from the analysis. Mean accuracies in physics are significantly lower compared to mathematics. Function types with negative values for either y intercept or slope also result in significantly lower mean accuracies indicating the difficulty students have with negative numbers in linear functions. A distractor analysis of the incorrect answers chosen by the students reveals three distinct dominant errors: concept switching, sign switching, and switching of the directly proportional function type and the function type with positive y intercept and positive slope.