Prospective mathematics teachers experience errors in solving straight-line equations, such as using unorthodox methods, answers that conflict with concepts and wrong calculations. This study aimed to analyze the difficulties of prospective mathematics teachers in algebraic material about straight-line equations. This research is descriptive qualitative research with a case study approach. The subjects in this study were students of the 3rd semester of the Mathematics Education Study Program, Widya Dharma University, Klaten, who had taken field analytic geometry courses. The data collection method in this study used the test method and the interview method. This study uses triangulation techniques to obtain valid data. The triangulation technique used is a triangulation method that compares data or information using different methods. The research instrument includes the main instrument, namely the researcher, whose role is to collect research data and auxiliary instruments in tests and interview guidelines. The data obtained from the interviews were analyzed using the analysis model of Miles, Huberman and Saldana, which includes data condensation, data presentation and drawing conclusions. The results of this study are that prospective mathematics teacher have difficulty in: (1) identifying which equations are straight lines and which ones are not, (2) explaining the concept of gradient, (3) proving the statement that two parallel lines have the same gradient, (4) prove the statement that two lines are perpendicular if the two gradients are multiplied the result is -1, (5) prove the formula for the equation of a straight line with a known gradient and a point through which it passes, and (6) prove the equation for a straight line if two are known the point through which. This study concludes that prospective mathematics teachers have difficulty in the material of straight-line equations.