C) III only
The y-intercept is 4. Therefore we have y=mx+4
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out I & II.
If you choose to go with the options directly, here's an approach.
y=mx+4. For the x-intercept, y=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+4 =0 would never be satisfied.
If x=6, we have 6m+4=0. A value of m=-2/3 would satisfy this equation.
Hope this helps.