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# In the rectangular co-ordinate system does the line k

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In the rectangular co-ordinate system does the line k [#permalink]  20 Mar 2011, 03:07
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Question Stats:

67% (01:20) correct 33% (00:00) wrong based on 15 sessions
In the rectangular co-ordinate system does the line k intersect quadrant II?

1) slope of line k is -1/6
2) the y-intercept of line k is -6

OA is provided.

[Reveal] Spoiler:
I am not sure how the slope alone can help solve this.

[Reveal] Spoiler: OA
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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 03:16
As you know the equation of a line is y=kx+b
II quadrant means that for x<0 y>0
(1) says that the line is y=-1/6x+b. Whatever b you have (positive or negative), this is some finite number. Taking x as low as you can (going to -infinity), you always could get -1/6*x as much positive as you need such that the sum -1/6x+b is positive. In other words, solving -1/6*x+b=0 you get the for any x<6b y is positive, obviously for some negative values of x this will also hold.
(2) says that y(0)=-6 which means that b=-6. Is the slope is positive, then such line will never intersect II quadrant. For example y=-6+x will never intersect it.

So (1) is sufficient, (2) is not. The answer is (A)
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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 04:30
1
KUDOS
The answer is A, I think you can visualize this without any calculation.

Also, please check MATH book, and Bunuel's tutorials where it's explained what type of lines with what signs pass from which quadrants.
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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 06:13
1
KUDOS
It's A.
1. A line with a negative slope always passes through second and fourth quadrant. Thus sufficient
Likewise A line with positive slope always passes through First and Third Quadrant.

2. this is insufficient, If the slope of the line is negative, then the line will touch the second quadrant to the left of the y axis & If the slope of the line is positive, or zero (parallel to the x axis), the the line will never touch the second quad.
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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 07:49
@subhashghosh pls can u send the link to bunuel's post

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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 21:34
1
KUDOS
@gmat1220, here you go :

math-coordinate-geometry-87652.html
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Re: rectangular co-ordinate system [#permalink]  20 Mar 2011, 22:18
@subhashghosh thanks so much!

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Re: rectangular co-ordinate system   [#permalink] 20 Mar 2011, 22:18
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