Simple Linear Regression
Simple linear regression uses one predictor:
$$y_i = \beta_0 + \beta_1 x_i + e_i, \qquad i = 1, \dots, n.$$The slope $\beta_1$ measures how the mean response changes with the predictor, while the intercept $\beta_0$ gives the fitted mean at $x=0$. In lecture, this appears in examples such as mortality versus temperature and the breast-cancer data.
The fitted line is used both for interpretation and for prediction within the observed range of $x$.