This study examines teachers' mathematical understanding of various representations of slope and their knowledge for teaching the concept of slope. Specifically examined in this research are the concept images and concept definitions of slope held by both preservice (N=18) and inservice (N=21) secondary mathematics teachers. Data collected include transcriptions of audiotaped interviews and surveys which are designed to probe teachers' knowledge of slope, their concept images and concept definitions, and their mathematical understanding. The process of analytic induction is the method used for analysis of the transcripts. Transcript analysis revealed patterns in individual teachers' responses as well as patterns in comparisons among various teachers' responses. The results of the mathematics survey provide a broad picture of secondary mathematics teachers' knowledge of the concept of slope and indicate general trends concerning the representations of slope. Contains 25 references. (DDR)