Đáp án:
$\begin{array}{l}
a)\left( d \right):y = \left( {2m + 1} \right).x + 3k - 1\\
\left( d \right)//y = x + 4\\
\Leftrightarrow \left\{ \begin{array}{l}
2m + 1 = 1\\
3k - 1 \ne 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m = 0\\
k \ne \dfrac{5}{3}
\end{array} \right.\\
Vậy\,m = 0;k \ne \dfrac{5}{3}\\
b)\left( d \right) \bot y = 2x - 1\\
\Leftrightarrow \left( {2m + 1} \right).2 = - 1\\
\Leftrightarrow 2m + 1 = - \dfrac{1}{2}\\
\Leftrightarrow m = - \dfrac{3}{4}\\
Vậy\,m = - \dfrac{3}{4}\\
c)\left( d \right) \cap y = 2 - 3x\\
\Leftrightarrow 2m + 1 \ne - 3\\
\Leftrightarrow 2m \ne - 4\\
\Leftrightarrow m \ne - 2\\
Vậy\,m \ne - 2
\end{array}$
