Is it D ?

Not at all sure but each statement says that the intersecting lines will have opposite signs in slope.
OA please ?

In the XY-coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?

1) The product of the x-intercepts of line L and K is positive.

2) The product of the y-intercepts of line L and k is negative.

This is a visualization question. The trick is to see the different ways the lines could be drawn.

Statement 1:
Line L has an x intercept at (1,0). Slope is positive.
Line K has an x intercept at (2,0). Slope is positive.
Positive * Positive = Positive

Line L has an x intercept at (1,0). Slope is positive.
Line K has an x intercept at (10,0). Slope is negative.
Positive * Negative = Negative.

Since the product can be both positive and negative, insufficient.

Statement 2:
Line L has a y intercept at (0,1). Slope is positive.
Line K has a y intercept at (0,-1). Slope is positive.
Positive * Positive = Positive

Line L has a y intercept at (0,10). Slope is negative.
Line K has an y intercept at (0,-1). Slope is positive.
Negative * Positive = Negative.

Since the product can be both positive and negative, insufficient.

Statements 1 and 2 together:
For the product of the x intercepts to be positive, both must be positive or both must be negative.
For the product of the y intercepts to be negative, one must be positive and the other must be negative.

If both x intercepts are negative, we won't be able to satisfy statement 2, because neither line will be able to pass through (4,3) and have a negative y intercept. Thus, both x intercepts must be positive.

So to satisfy both statements, we need 2 positive x intercepts, 1 positive y intercept, and 1 negative y intercept:
A positive x intercept and a positive y intercept will yield a negative slope.
A positive x intercept and a negative y intercept will yield a positive slope.
Negative * Positive = Negative.
Suffficient.

The correct answer is C.