In some modeling scenarios, the regression intercept is restricted to zero, representing a model with no constant term. The least-squares slope for this model is given by $\beta_1 = \frac{\sum x_i y_i}{\sum x_i^2}$. Given three data points $(2, 5)$, $(3, 7)$, and $(5, 12)$, compute the slope $\beta_1$ of the zero-intercept line.