A transformation $T: \mathbb{R}^2 \to \mathbb{R}^2$ is defined by the matrix $A = \begin{pmatrix} 1 & k \\ 0 & 1 \end{pmatrix}$. For what value of $k$ does this shear transformation map the line $y = x$ to the line $y = \frac{1}{2}x$?