Do you mean the line K passes through second quadrant?
if that is the case statement 1 is sufficient to say yes
but from second statement we cannot conclude any thing as the line might be parallel to x axis ie the line could be y=-6

ans A

can you please confirm that whether it is correct or I have mis interpreted the question?

yes the answer is A and you interpreted it correct . I understand how Statement 2 is insuff , could you please explain how statement 1 is sufficient please? thanks

from the first statement we get slope is -1/6 ..hence the line makes an obtuse angle with x-axis hence when extended infinitely it will pass through second,fourth and either first or third quadrant.
Let me know if this clarifies why statement 1 is sufficient .

nisha.menon294 wrote:In a rectangular co-ordinate system does the line K intersect the second quadrant ?

1) the slope of k is -1\6
2) the y intercept ok k is -6

Slope of a line = -(y-intercept)/ (x-intercept).

(1) compared with the slope formula, suggests that intercepts are either both positive or both negative. In both cases, the line would intersect the second quadrant. Sufficient

(2) With a negative y-intercept, the line would intersect the second quadrant if it's x-intercept is also negative, otherwise it won't intersect the second quadrant. Insufficient

[spoiler]A[/spoiler]

we just had a similar discussion in this question - does this informaiton help? https://www.beatthegmat.com/post246538.html