General formula y = mx+c (m is slope)
Passes through (0,0). Put in the formula c=0
Thus y = mx
passes through (a,b) then b = ma
1. slope is -ve
Then b = -m*a then (a,b) can lie in 2nd or 4th quadrant.
if 2nd then b +ve
if 4th then b -ve
Not sufficient.
2. a<b
we cannot say anything as this can happen in all of the quadrants. Not sufficient.
Combine both only 2nd qudarant will satisfy as a will be -ve and b will be +ve. Thus sufficient.
PS: Slope negative and line must through origin then the line must be in 2nd to 4th quadrant,
See below 3 lines are there in the picture.
1. Red: Angle subtended by this line with X axis is less than 90. Slope is +ve. (Remember trigonometry? TAN(angle) is the slope)
2. Blue: Angle subtended by this line with X axis is equal to 90. Slope is infinite(cannot be determined).
3. Green: Angle subtended by this line with X axis is greater than 90. Slope is -ve.
