3. Given points $A(1,2)$ and $B(2,1)$, the line segment $AB$ intersects with the line $y=3x+b$. Then the range of values for $b$ is ( ).
(A) $b>-5$
(B) $b<-1$
(C) $-5<b<-1$
(D) $-5 \leqslant b \leqslant-1$
3. D.

When the line $y=3 x+b$ passes through point $A$, we have $2=3+b$, solving for $b$ gives $b=-1$;

When the line $y=3 x+b$ passes through point $B$, we have $1=6+b$, solving for $b$ gives $b=-5$.
Therefore, options $(\mathrm{A})$, $(\mathrm{B})$, and $(\mathrm{C})$ are eliminated.