In xy plane, what is the y intercept of line l ?
1) The slope of line l is 3 times y intercept.
2) The x intercept of line l is -1/3.






actually, if you play around with statement 1, you'll notice that it actually implies what's in statement 2.
viz., if statement 1 is true , then we have m = 3c --> y = 3cx + c.
therefore, if we want to find the x-intercept of that line, we'd set y = 0, and we'd have
0 = 3cx + c
0 = c(3x + 1)
therefore, either c = 0 or x = -1/3.
we can't have c = 0, since that would give a horizontal line; if we had a horizontal line, then every point would be an "x intercept". (you may want to check the problem statement again -- there should be some sort of statement that says that the line should be non-horizontal.)
therefore, the x intercept must be -1/3.
so, if you have statement 1, then statement 2 actually adds no new information at all.


some coordinate geometry statements are easy to work with algebraically, but nearly impossible to work with visually; others are easy to work with visually, but very hard or nearly impossible to work with algebraically.
therefore,
you should develop facility with both the algebraic and the visual approaches to coordinate geometry.




"does line k intersect quadrant II?"
1) k=-1/6
2)y intercept = -6


in any case, ALGEBRA IS NOT AN EFFICIENT WAY TO SOLVE MOST GMAT PROBLEMS ABOUT SLOPES AND QUADRANTS. YOU SHOULD LEARN TO CONCEPTUALIZE SLOPES. in other words, you should internalize the idea of positive slope vs. negative slope vs. zero slope vs. undefined slope, and you should be able to think about what those slopes LOOK like.
if you realize that a slope of -1/6 goes up to the left and down to the right, then it's easy to see that it eventually has to go into the upper left quadrant. compared to that, why would anyone want to bother with all that algebra?