In the xy-plane, the line k passes through the origin and through the

Target question: Is b (the y-coordinate of the point on the line) positive?

Given: Line k passes through the origin and through the point (a,b)

Statement 1: The slope of line k is negative
There are several lines and points that satisfy statement 1. Here are two:

Case a:

In this case, b (y-coordinate) is positive. So, the answer to the target question is YES, b is positive

Case b:

In this case, b (y-coordinate) is negative. So, the answer to the target question is NO, b is NOT positive

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a < b
There are several lines and points that satisfy statement 2. Here are two:

Case a:

In this case, b (y-coordinate) is positive. So, the answer to the target question is YES, b is positive

Case b:

In this case, b (y-coordinate) is negative. So, the answer to the target question is NO, b is NOT positive

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the slope of line k is negative. This means line k passes through quadrants II and IV.

In quadrant II, a (the x-coordinate) is always negative, and b (the y-coordinate) is always positive
In quadrant IV, a (the x-coordinate) is always positive, and b (the y-coordinate) is always negative

Statement 2 tells us that a < b
This means that the point (a,b) must be in quadrant II (because, all points in quadrant IV are such that the x-coordinate (a) is greater than the y-coordinate (b)
If point (a,b) is in quadrant II, we can be certain that b (the y-coordinate) is positive
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent