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# IN the xy-plane, the line k passes thru the origin and thru

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Senior Manager
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IN the xy-plane, the line k passes thru the origin and thru [#permalink]

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15 Sep 2006, 17:17
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IN the xy-plane, the line k passes thru the origin and thru the point(a,b), where ab != 0. Is b positive?

1) the slope of line k is negative

2) a <b
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15 Sep 2006, 17:47

Question : b > 0?

General Eqn of line passing through origin : y = mx

S1: m < 0

As line passes through (a, b)
b = ma
or b/a = m
As m < 0, b/a < 0

Either
b < 0, a > 0 or
b > 0, a < 0
Not sufficient.

S2: a < b
b = ma

Let a = -1, b = 2 if m = -1, b > 0
if m = 1, b < 0
Not sufficient.

S1& S2:
m < 0 and a < b
b = ma
or b/a = m < 0 => b/a < 0

Either b < 0, a > 0 Not possible as a < b,
or b > 0, a < 0, Posisble and only case.

Sufficient:

Senior Manager
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16 Sep 2006, 02:28
Folks, this is again simple.

Given the line passes through (0,0) and (a,b)
Hence it's slope is b/a [By the way slope of a line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)]

Statement 1: Slope is negative
ie b/a<0 => a and b are of opposite signs, but we can't conclude that b <0

Statment 2: a < b , Clearly this alone is not sufficient.

Now combining both we know that a and b are of opposite signs and a<b
So a is -ve and b is +ve

Regards,
_________________

Last edited by cicerone on 25 Sep 2008, 01:07, edited 1 time in total.
Senior Manager
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17 Sep 2006, 20:16
OA is C .... Great explainations thanks
17 Sep 2006, 20:16
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# IN the xy-plane, the line k passes thru the origin and thru

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