Which of the following is an equation for the line that passes through$\left(\mathbf{2}\mathbf{,}-\mathbf{5}\right)$ and is perpendicular to $\mathbf{2}x+\mathbf{4}y=\mathbf{8}$?

$$\begin{gathered} \mathbf{A}\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{10} \\ \mathbf{B}\mathbf{y}\mathbf{=}\mathbf{-}\frac{1}{2}\mathbf{x}\mathbf{-}\mathbf{4} \\ \mathbf{C}\mathbf{y}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{9} \\ \mathbf{D}\mathbf{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{1} \end{gathered}$$

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