Đáp án:
$\begin{array}{l}
a)\left( d \right)//y = - 2x + 5\\
\Rightarrow \left\{ \begin{array}{l}
a = - 2\\
b \ne 5
\end{array} \right.\\
\Rightarrow \left( d \right):y = - 2x + b\\
Do:A \in \left( d \right)\\
\Rightarrow 2 = \left( { - 2} \right).\left( { - 1} \right) + b\\
\Rightarrow b = 0\left( {tmdk} \right)\\
\text{Vậy}\,\left( d \right):y = - 2x\\
c)d \bot y = - 2x + 5\\
\Rightarrow a.\left( { - 2} \right) = - 1\\
\Rightarrow a = \dfrac{1}{2}\\
\Rightarrow \left( d \right):y = \dfrac{1}{2}x + b\\
C\left( {2; - 3} \right) \in \left( d \right)\\
\Rightarrow - 3 = \dfrac{1}{2}.2 + b\\
\Rightarrow b = - 4\\
\text{Vậy}\,\left( d \right):y = \dfrac{1}{2}x - 4\\
e)d \equiv y = 2x + a + 3\\
\Rightarrow \left\{ \begin{array}{l}
a = 2\\
b = a + 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
a = 2\\
b = 5
\end{array} \right.\\
\Rightarrow \left( d \right):y = 2x + 5
\end{array}$
