I have a dataset that has x,y coordinates for 2 ends of an object over
time.
I can plot the end points in gnuplot with:

plot "inputfile" using 6:8 title "ballast", \
     "inputfile" using 14:16 title "payload"

But I would like to have a line between these 2 points but not
connecting to any other points on earlier or later lines in the file. 
How do I do this?

Sample 3 lines from "inputfile" follows:
T1 tether  time 30 balx 1390.64 baly 6842.84 cmx 1377.44 cmy 6827.3
payx 1064.46 payy 6458.65
T1 tether  time 61 balx 1156.51 baly 6886.95 cmx 1145.21 cmy 6870.02
payx 876.83 payy 6467.31
T1 tether  time 91 balx 928.5 baly 6921.96 cmx 919.16 cmy 6903.84 payx
698.31 payy 6473.64