Đáp án:
$\begin{array}{l}
1)A,B \in y = a.x + b\\
\Rightarrow \left\{ \begin{array}{l}
3 = 2a + b\\
4 = - a + b
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
3a = - 1\\
b = 3 - 2a
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - \dfrac{1}{3}\\
b = \dfrac{{11}}{3}
\end{array} \right.\\
\text{Vậy}\,a = - \dfrac{1}{3};b = \dfrac{{11}}{3}\\
2)y = a.x + b//y = 2x - 3\\
\Rightarrow a = 2;b \ne - 3\\
Do:M\left( {1;2} \right) \in y = 2x + b\\
\Rightarrow 2 = 2.1 + b\\
\Rightarrow b = 0\left( {tm:b \ne - 3} \right)\\
\text{Vậy}\,a = 2;b = 0\\
3)y = a.x + b \bot y = - 4x + 3\\
\Rightarrow a.\left( { - 4} \right) = - 1\\
\Rightarrow a = \dfrac{1}{4}\\
\Rightarrow y = \dfrac{1}{4}x + b\\
Do:N\left( { - 1;3} \right) \in y = \dfrac{1}{4}x + b\\
\Rightarrow 3 = \dfrac{1}{4}.\left( { - 1} \right) + b\\
\Rightarrow b = \dfrac{{13}}{4}\\
\text{Vậy}\,a = \dfrac{1}{4};b = \dfrac{{13}}{4}\\
4)Goi:A = {d_1} \cap {d_2}\\
\text{Xét}:x + 2 = - x + 7\\
\Rightarrow 2x = 5\\
\Rightarrow x = \dfrac{5}{2}\\
\Rightarrow y = x + 2 = \dfrac{9}{2}\\
\Rightarrow A\left( {\dfrac{5}{2};\dfrac{9}{2}} \right)\\
\text{3 đường thẳng đồng quy thì} \Rightarrow A \in {d_3}\\
\Rightarrow \dfrac{9}{2} = \dfrac{5}{2}m - 4\\
\Rightarrow \dfrac{{17}}{2} = \dfrac{5}{2}m\\
\Rightarrow m = \dfrac{{17}}{5}\\
\text{Vậy}\,m = \dfrac{{17}}{5}
\end{array}$
