The perpendicular bisector of the line segment joining P(1,4) and Q(k,3) has y-intercept-4. Then a possible value of k is 

${\perp }^r$ bisector of PQ is  $(x_1-x_2)x+(y_1-y_2)y=\frac{1}{2}[(x_1^2+x_2^2)-(y_1^2+y_2^2)]$

$\begin{array}{l}(1-k)x+(4-3)y=\frac{1}{2}((1+6)-(k^2+9))\\ \Rightarrow (1-k)x+y=\frac{(8-k^2)}{2}\\ y-\mathrm{int}ercept=-4\\ \frac{8-k^2}{2}=-4\Rightarrow 8-k^2=-8\Rightarrow k^2=16,k=\pm 4\end{array}$