In this work, we explore some applications of mathematics in the development and usage of supervised learning algorithms with a strong focus on linear regression models. Subsequently, we look at the mathematical foundations essential for supervised learning, which include linear algebra, probability theory, calculus, optimization, statistics, and geometry. For a concrete illustration of the applications of mathematics in supervised learning, this work employs simple and multiple linear regression models using data that is about pH of pure water. Through these examples, we demonstrate how mathematical techniques are applied in formulating, estimating and evaluating linear regression models. Key processes such as least squares estimation and statistical inference are highlighted to show their critical application in parameter estimation and model validation. The findings underscore the importance of mathematical rigor in ensuring accuracy and interpretability of supervised learning models.