\begin{enumerate}
\item $A\coord{-5}{3}$ et $B\coord{2}{-2}$.
\begin{itemize}
\item
$A\in(d)\iff f(-5)=3\iff a\times(-5)+b=3\iff-5a+b=3$; 

\item
$B\in(d)\iff f(2)=-2\iff a\times2+b=-2\iff2a+b=-2$. 
\end{itemize}
On a donc :
\begin{align*}
\systeme[ab]{-5a+b=3@L_1,2a+b=-2@L_2}
& \iff \sysautonum{L_{*}\longleftarrow}\systeme[ab]{7a=-5@L_2-L_1,7b=-4@2L_1+5L_2}\\
& \iff \syslineskipcoeff{2}\systeme[ab]{a=-\dfrac{5}{7},b=-\dfrac{4}{7}}
\end{align*}

\underline{Ainsi, $f(x)=-\dfrac{5}{7}x-\dfrac{4}{7}$.}

\newpage

\item $A\coord{2}{-1}$ et $B\coord{-2}{5}$.

\begin{itemize}
\item
$A\in(d)\iff f(2)=-1\iff a\times2+b=-1\iff2a+b=-1$; 

\item
$B\in(d)\iff f(-2)=5\iff a\times(-2)+b=5\iff-2a+b=5$. 
\end{itemize}
On a donc :
\begin{align*}
\systeme[ab]{2a+b=-1@L_1,-2a+b=5@L_2}
& \iff \sysautonum{L_{*}\longleftarrow}\systeme[ab]{4a=-6@L_1-L_2,2b=4@L_1+L_2}\\
& \iff \syslineskipcoeff{2}\systeme[ab]{a=-\dfrac{3}{2},b=2}
\end{align*}

\underline{Ainsi, $f(x)=-\dfrac{3}{2}x+2$.}

\item $A\coord{9}{-7}$ et $B\coord{-7}{9}$.

\begin{itemize}
\item
$A\in(d)\iff f(9)=-7\iff a\times9+b=-7\iff9a+b=-7$; 

\item
$B\in(d)\iff f(-7)=9\iff a\times(-7)+b=9\iff-7a+b=9$. 
\end{itemize}
On a donc :
\begin{align*}
\systeme[ab]{9a+b=-7@L_1,-7a+b=9@L_2}
& \iff \sysautonum{L_{*}\longleftarrow}\systeme[ab]{16a=-16@L_1-L_2,16b=32@7L_1+9L_2}\\
& \iff \systeme[ab]{a=-1,b=2}
\end{align*}

\underline{Ainsi, $f(x)=-x+2$.}
\end{enumerate}