The aim of this study is to analyze eight grade students' mathematizing processes of the concept of slope in light of the teaching process designed based on Realistic Mathematics Education. Participants of this design based research study were chosen via purposeful sampling in accordance with results of an open-ended test intended for prerequisite information before design teaching-learning environment. Survey data was acquired from open-ended test, researcher log, individual and group study papers and clinical interviews. Contexts, which provide opportunities to reflect preliminary conceptions of slope to teaching process are revealed. Conceptualization process of slope as ratio started with the need to be base of informal linear constant. Then it develops with the need of measurement of slope. Students reinvent that the slope is also an algebraic ratio by reflecting geometric ratio representation to coordinate plane. Designed teaching in this study was revealed that mathematization is important in transition among representations. Development of right triangle model occurred in three phases: (i) a context-dependent interpretive tool, (ii) a physical tool used to calculate the slope, (iii) a cognitive tool that that is no longer needed to be represented physically.