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Lines k and l lie in the xy-plane. Is the slope of line k [#permalink]
03 Jan 2008, 08:25
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Lines k and l lie in the xy-plane. Is the slope of line k less than the slope of line l ? (1) The y-intercept of line k is greater than the y-intercept of line l. (2) Lines k and l intersect at the point (1, 6)
Each statement alone is insufficient for obvious reasons.
Now taken together:
We know that they cross at (1,6) which is in the first quadrant and very close to the y-axis.
it says that K has a greater y-intercept. Now picture the lines meeting at (1,6):
if both slopes are positive then K will have a smaller slope (ie less step). the flatter the slope the higher up it will cross. a slope approaching a flat line will get very close to crossing the y-axis at 6, whereas a very steep slope could potentially cross the y-axis at a negative point!
now if both slopes are negative the opposite is true. the steeper of the two negative slopes will cross at a greater point. thus, if K crosses higher up and they're both negative it will be a smaller number (-3 vs -1 sort of thing).
now if one slope is negative and one slope is positive the negative slope will ALWAYS cross at a higher point. so in this case K would always be the negative one, which is always a smaller number than a positive number.
I really can't explain it much better than that. It's something you have to visualize. maybe draw out the coordinate plane and sketch out some combinations to see what I mean. sorry if I'm not being terribly helpful here, but I didn't use any math or tricks to get this answer.
From S1 we can not conclude anything because slope ob both lines can be anything From S2 we can not conclude anything either. From S1 and S2, and drawing all the possible lines l and k we can conclude that it is sufficient