This paper explores the various approaches to solving mathematical and applied problems through graphical methods. Graphs provide a visual representation that simplifies complex relationships, enabling learners and professionals to interpret data, detect patterns, and solve problems effectively. The study outlines several key graphical strategies, including coordinate plotting, function graphing, systems of equations analysis, and real-world data modeling. The effectiveness of each method is discussed through examples, and their relevance in education and applied fields is emphasized. The paper concludes by underlining the importance of graphical literacy in developing analytical thinking and problem-solving skills.

Graphical methods, problem solving, coordinate system, function graphing, data visualization, systems of equations, mathematical modeling

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077

Biehler, R., & Kempen, L. (2015). Supporting students' understanding of function and graph through technology-enhanced instruction. Journal of Mathematics Education at Teachers College, 6(2), 1–10.

Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 397–430). Lawrence Erlbaum Associates.

Larson, R., & Edwards, B. H. (2013). Precalculus: Real mathematics, real people (6th ed.). Brooks/Cole Cengage Learning.

Stewart, J. (2016). Calculus: Early transcendentals (8th ed.). Cengage Learning.

Tall, D. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9781139565202

Tufte, E. R. (2001). The visual display of quantitative information (2nd ed.). Graphics Press.

Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Information Age Publishing.