[tex]\boxed{f(x)=ax+b}[/tex]
[tex]f(3)=5\ \therefore\ a(3)+b=5\ \therefore\ \boxed{3a+b=5}\ (i)[/tex]
[tex]f(-2)=-5\ \therefore\ a(-2)+b=-5\ \therefore\ \boxed{2a-b=5}\ (ii)[/tex]
[tex](i)+(ii)\ \to\ 3a+b+2a-b=5+5\ \therefore\ \boxed{a=2}[/tex]
[tex]b=2a-5\ \therefore\ b=2(2)-5\ \therefore\ \boxed{b=-1}[/tex]
[tex]\boxed{f(x)=2x-1}[/tex]
