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.

i.e. mx+4=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.