Straight line passes through the points (a,b) and (c,d). Is

Statement 1.
(a-c)(b-d)<0.
1) a-c>0, then b-d<0
2) a-c<0, then b-d>0
It means that when x increases y decreses=> the line is sloping down
or mathematically, the slope \(\frac{a-c}{b-d}<0\) since numerator and denominator have opposite signs.
SUFFICIENT

Statement 2 is sufficient
If the product of intercepts is positive, intercepts should be of the same sign => this is only the case when a line is sloping down. If the line is sloping "up" the product of the intercepts is negative or zero. Note: if it is said that the product is zero, we can't determine if the line is loping up or down since both are possible.
SUFFICIENT.
Mathematically it can be also shown:
\(y=\alpha\times x +\beta\)
Point (0,\(\beta\)) is the Y intercept
Point \((- \frac{\beta}{\alpha},0)\)is the X intercept
\(-\frac{\beta}{\alpha}\times \beta=-\frac{\beta^2}{\alpha}>0\)...it is only possible when \alpha<0...

suppose the line is:

y=s*x+k

b=as+k
d=cs+k

s=(b-d)/(a-c)

1) is suff

for 2), just draw the line in the xy plane, it is suff

the answer is D

Both statements are sufficient alone
OA is D