for x > 4, x/(x-4) > 1, so the slopes will be positive, leveling out
for x < 4, the slopes will be negative, leveling out.
The slopes will be approaching vertical at x=4.
Looks like III.
See
http://www.wolframalpha.com/input/?i=vector+plot&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorfunction%22}+-%3E%22{x,x-4}%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotvariable1%22}+-%3E%22x%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotlowerrange1%22}+-%3E%22-10%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotupperrange1%22}+-%3E%2210%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotvariable2%22}+-%3E%22y%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotlowerrange2%22}+-%3E%22-10%22&rawformassumption={%22F%22,+%22VectorPlot%22,+%22vectorplotupperrange2%22}+-%3E%2210%22&rawformassumption={%22MC%22,+%22%22}+-%3E+{%22Calculator%22}&rawformassumption={%22MC%22,%22%22}-%3E{%22Formula%22}
dy/dx=x/(x-4)
I.will have a slope field with negative slopes in quadrant I
II.will have a slope field with positive slopes in all quadrants
III.will produce a slope field with columns of parallel tangents
2 answers
Answer is none of these