Semi-supervised learning (SSL) has attracted growing interest due to its ability to incorporate information from a large set of $N$ unlabeled data to enhance the estimation and prediction performance of supervised learning (SL) based on a smaller set of $n$ labeled data. In this work, we derive the minimax learning rates for both estimation and prediction in SSL in the context of high-dimensional linear regression. Noting that the benefit of unlabeled data arises when the covariates contain information that is shared with the regression structure. To systematically examine the contribution of unlabeled data, we consider three distinct covariance structures: the eigenvalue decay model, the spiked covariance model, and factor analysis models. Our analysis yields several interesting findings: (a) When SL alone cannot achieve accurate estimations/predictions and $N$ is significantly larger than $n$, SSL can outperform SL by achieving higher-order improvements in both estimation and prediction accuracy; (b) Feature-extraction-based SSL generally outperforms imputation-based SSL, except in cases where the dimension $p$ is very large and $N$ is small relative to $n$. In terms of prediction accuracy, the feature-extraction approach consistently provides superior performance. These theoretical findings are further supported by numerical experiments.