Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope; graphical understanding; ratio and rate; and proportional reasoning. In light of this discussion, the design of a mathematical resource to help give students a deep understanding of slope is described. The resource was used at one university, amongst Chinese first-year undergraduate science and engineering students. Evidence would suggest that those students who did not evidence a correct understanding of all the aspects of slope (deep understanding) before completing the resource improved their understanding of these aspects upon completion of the resource.