Find \( a \) and \( b \)
If
\[ f(x)=ax+b \]
where \(a\) and \(b\) are integers,
\[ f(-1)=-5 \]
and
\[ f(3)=3, \]
then \(a\) and \(b\) are equal to
(a) \(a=-3,\; b=-1\)
(b) \(a=2,\; b=-3\)
(c) \(a=0,\; b=2\)
(d) \(a=2,\; b=3\)
Given,
\[ f(-1)=-a+b=-5 \]
and
\[ f(3)=3a+b=3 \]
Subtracting,
\[ 4a=8 \]
\[ a=2 \]
Putting in
\[ -a+b=-5 \]
\[ -2+b=-5 \]
\[ b=-3 \]
Therefore,
\[ \boxed{a=2,\; b=-3} \]
\[ \boxed{\text{Correct Answer: (b)}} \]