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

Hi!

(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)!

Stuart Kovinsky wrote:

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

Hi!

(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)!

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.

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