The quality of knowledge underlying students' algebraic thinking is a major concern of K-12 mathematics teaching and reform-driven curriculum documents. In this paper the author examines this issue by characterizing a group of high school students' algebraic knowledge and patterns of use of that knowledge during the solution of selected problems. Results show that these students tended to show acceptable levels of proficiency with problems that involved substitution of values and simplification of equations. Students experienced difficulties with the interpretation of algebraic relations. Multiple regression analysis showed that knowledge about equations and pattern formation was a predictor of students' success at interpretation of graphs of linear functions. These results are interpreted as suggesting that understanding and analysis of graphs could be facilitated by teaching approaches that focus on the construction of robust schemas about patterns and symbolic relations in algebra. (Contains 7 tables.)