Đáp án:
Do A, B nằm trên đường thẳng nên ta thay tọa độ của chúng vào pt đt sẽ thỏa mãn
$\begin{array}{l}
1)\left\{ \begin{array}{l}
- 7 = \left( {a - 2} \right).1 + b + 5\\
5 = \left( {a - 2} \right).4 + b + 5
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a - 2 + b + 5 = - 7\\
4a - 8 + b + 5 = 5
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a + b = - 10\\
4a + b = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 6\\
b = - 16
\end{array} \right.\\
\Rightarrow y = 4x - 11\\
2)\left\{ \begin{array}{l}
6 = \left( {a - 2} \right).2 + b + 5\\
- 9 = \left( {a - 2} \right).3 + b + 5
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
2a - 4 + b + 5 = 6\\
3a - 6 + b + 5 = - 9
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
2a + b = 5\\
3a + b = - 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - 13\\
b = 31
\end{array} \right.\\
\Rightarrow y = - 15x + 36\\
3)\left\{ \begin{array}{l}
0 = \left( {a - 2} \right).4 + b + 5\\
- 1 = \left( {a - 2} \right).3 + b + 5
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
4a - 8 + b + 5 = 0\\
3a - 6 + b + 5 = - 1
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
4a + b = 3\\
3a + b = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 3\\
b = - 9
\end{array} \right.\\
\Rightarrow y = x - 4
\end{array}$
