In what ratio does the line $3x+y=9$ divide the segment joining A(1, 3) and B(2, 7)?

Let the ratio be $m:n$, so the dividing point is $(\frac{2m+n}{m+n},\frac{7m+3n}{m+n})$. Substituting in $3x+y=9$ gives $3(2m+n)+(7m+3n)=9(m+n)$, so $13m+6n=9m+9n,4m=3n$ and $m:n=3$ : 4. The point is $(\frac{10}{7},\frac{33}{7})$ and indeed 3 $\cdot \frac{10}{7}+\frac{33}{7}=9$. The answer 4 : 3 inverts $m$ and $n$; 3 : 7 quotes $m:(m+n)$; 1 : 1 assumes the line passes through the midpoint (1.5, 5), but $3(1.5)+5=9.5$, not 9.