This study investigates the relationship between logical thinking structures and the ability to construct and interpret line graphs. Seventy-two subjects in 7th, 9th, and 11th grades were administered individual Piagetian tasks to assess five specific mental structures: (Euclidean spatial structures) (a) Placement and Displacement of Objects (maintaining horizontal and vertical reference frames) and (b) One–One Multiplication of Placement and Displacement Relations (coordinate systems); (c) Multiplicative Measurement; (d) Multiplicative Seriation; and (e) Proportional Reasoning. Graphing abilities were assessed by having the subjects construct and interpret numerous graphs of varying content and difficulty. To minimize the researcher's guesses about interpretation, each subject's answers and reasons were subsequently explored during a clinical interview. The results indicate significant relationships of logical thinking to graphing ability. Multiplicative seriation, multiplicative measurement, and Euclidean spatial structures positively influenced graphing abilities. Subjects who showed evidence of proportional reasoning did significantly better on many graphing situations including choosing the part of the graph with the greatest “rate of change.” Locating points on a graph without a grid was significantly related to horizontal/vertical frames of reference. Students who did not possess the logical thinking structures were more likely to be dependent upon, and influenced by, perceptual cues and less able to interpret or construct graphs correctly.