This study presents a classroom proposal to integrate concepts from Graph Theory and Linear Algebra in complete bipartite graphs, linking adjacency and Laplacian matrices and determining their eigenvalues. Students engage in exploration activities using GeoGebra software, starting with specific cases and completing tables and questionnaires to identify patterns in the eigenvalues of adjacency and Laplacian matrices of complete bipartite graphs. This process leads to generalization, allowing students to abstract properties from observations and experimentation. The learning experience bridges the concrete and symbolic, introducing students to research. The study explores the regularities in eigenvalues of adjacency and Laplacian matrices of complete bipartite graphs. Students use GeoGebra to generate matrices for different values of m, analyze the results, and formulate conjectures. The process involves identifying patterns, verifying conjectures, and generalizing findings. The use of GeoGebra facilitates dynamic exploration, enhancing students' understanding of algebraic concepts and promoting autonomous learning. The study highlights the importance of integrating technology in mathematics education, as it supports dynamic exploration, enhances motivation, and promotes critical thinking. It also emphasizes the role of inductive reasoning in mathematical discovery and the value of collaborative learning in developing mathematical thinking. The integration of technology in education is essential for motivating students, making lessons more innovative, and fostering autonomous learning. The study concludes that the use of GeoGebra in teaching mathematics provides significant benefits, including improved understanding of abstract concepts and enhanced problem-solving skills.This study presents a classroom proposal to integrate concepts from Graph Theory and Linear Algebra in complete bipartite graphs, linking adjacency and Laplacian matrices and determining their eigenvalues. Students engage in exploration activities using GeoGebra software, starting with specific cases and completing tables and questionnaires to identify patterns in the eigenvalues of adjacency and Laplacian matrices of complete bipartite graphs. This process leads to generalization, allowing students to abstract properties from observations and experimentation. The learning experience bridges the concrete and symbolic, introducing students to research. The study explores the regularities in eigenvalues of adjacency and Laplacian matrices of complete bipartite graphs. Students use GeoGebra to generate matrices for different values of m, analyze the results, and formulate conjectures. The process involves identifying patterns, verifying conjectures, and generalizing findings. The use of GeoGebra facilitates dynamic exploration, enhancing students' understanding of algebraic concepts and promoting autonomous learning. The study highlights the importance of integrating technology in mathematics education, as it supports dynamic exploration, enhances motivation, and promotes critical thinking. It also emphasizes the role of inductive reasoning in mathematical discovery and the value of collaborative learning in developing mathematical thinking. The integration of technology in education is essential for motivating students, making lessons more innovative, and fostering autonomous learning. The study concludes that the use of GeoGebra in teaching mathematics provides significant benefits, including improved understanding of abstract concepts and enhanced problem-solving skills.