$25 \cdot 3$ In the $x O y$ rectangular coordinate plane, draw different lines passing through the point $(3,4)$ and the trisection points of the line segment with endpoints $(-4,5),(5,-1)$, one of the line equations is
(A) $3 x-2 y-1=0$.
(B) $4 x-5 y+8=0$.
(C) $5 x+2 y-23=0$.
(D) $x+7 y-31=0$.
(E) $x-4 y+13=0$.
(21st American High School Mathematics Examination, 1970)
[Solution] According to the section formula, the trisection points of the line segment with endpoints $(-4,5),(5,-1)$ are: $P(-1,3), Q(2,1)$.
The equations of the lines passing through the points $(3,4)$ and $P, Q$ are respectively
$$
x-4 y+13=0 \text { and } \quad 3 x-y-5=0 .
$$

Therefore, the answer is $(E)$.