In the xy-coordinate system, do any points on line k lie in quadrant III?
(1) Line k has y-intercept 2
(2) Line k has slope 2/3
Co-ordinate question from BTG practice questions
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Hi!r2kins wrote:In the xy-coordinate system, do any points on line k lie in quadrant III?
(1) Line k has y-intercept 2
(2) Line k has slope 2/3
(1) is insufficient, because it doesn't tell us anything else about the line. It could simply be the line y=2, in which case it wouldn't pass through quadrant III, or it could be any line with a positive slope, in which case it would pass through the quadrant.
(2) tells us that the line has a positive slope. You can either reason out that this is sufficient (by drawing a lot of lines and seeing that it's always true), or you remember a rule about lines in the x-y plane:
Any line with a positive slope must pass through quadrants I and III; and
any line with a negative slope must pass through quadrants II and IV.
Since our line has a positive slope, it must pass through quadrant III, so (2) is sufficient.
(2) is sufficient alone, (1) is not: choose (B)!
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Hi Stuart. I went by the rule stated by you. It just indicates that line could either pass through quandrant I or III. We can NOT conlusively say that it will pass though III.Stuart Kovinsky wrote:Hi!r2kins wrote:In the xy-coordinate system, do any points on line k lie in quadrant III?
(1) Line k has y-intercept 2
(2) Line k has slope 2/3
(1) is insufficient, because it doesn't tell us anything else about the line. It could simply be the line y=2, in which case it wouldn't pass through quadrant III, or it could be any line with a positive slope, in which case it would pass through the quadrant.
(2) tells us that the line has a positive slope. You can either reason out that this is sufficient (by drawing a lot of lines and seeing that it's always true), or you remember a rule about lines in the x-y plane:
Any line with a positive slope must pass through quadrants I and III; and
any line with a negative slope must pass through quadrants II and IV.
Since our line has a positive slope, it must pass through quadrant III, so (2) is sufficient.
(2) is sufficient alone, (1) is not: choose (B)!
On the other hand, if we consider both the statements together, we can conclusively say that the line passes through I, and hence does not pass through III.
I know I am missing something in my reasoning here. It would be a great help if you could help me pinpoint the flaw.
thanks