[tex]\displaystyle\\
f(3) = 5 \\
f(7) = -4\\\\
\texttt{Solve:}\\\\
f(x)=ax+b ~~~\Longleftrightarrow~~~ y=ax+b~~~\Longleftrightarrow~~~ ax+b-y=0\\\\
-------\\
3a+b-5=0~~~(E1)\\
7a+b+4=0~~~(E2)\\
---\\
E2 - E1\\
4a+9=0\\
4a =-9\\\\
\boxed{a = -\frac{9}{4} = -2,25}\\\\
3\times \Big(-\frac{9}{4}\Big) + b -5 = 0\\\\
-\frac{27}{4} -5+ b = 0\\\\
\frac{-27-20}{4} + b = 0\\\\
-\frac{47}{4} + b = 0\\\\
\boxed{b = \frac{47}{4} = 11,75}[/tex]
