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) Line k has y-intercept 2
(2) Line k has slope 2/3
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- quadrant system
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)!
