In the xy-plane, if line k has negative slope, is the

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In the xy-plane, if line k has negative slope, is the [#permalink]

15 Apr 2011, 20:19

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In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

Please provide explanation. Thanks!

[Reveal] Spoiler: OA

Last edited by skbjunior on 16 Apr 2011, 04:15, edited 1 time in total.

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Re: DS Coordinate Geom [#permalink]

15 Apr 2011, 21:15

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skbjunior wrote:

(1) Not Sufficient.

Attachment:

x_intercept_less_than_y.png [ 8.46 KiB | Viewed 673 times ]

(2)Not Sufficient.

Attachment:

slope_less_than_minus_2.png [ 8.55 KiB | Viewed 673 times ]

(3)Combining both.
It should always be to the right of the blue line.
Sufficient.

Attachment:

combining_both.png [ 7.34 KiB | Viewed 674 times ]

Ans: "C"

y=-2x+C

y-intercept
y=C

x-intercept
x=\frac{C}{2}

C>\frac{C}{2}
C-\frac{C}{2}>0
2C-C>0
C>0

Even for a slope of "-2", the y-intercept C has to be more than "0" or +ve to satisfy both statements.
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Re: DS Coordinate Geom [#permalink]

15 Apr 2011, 21:24

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My take (1) and (2) are insufficient :

Y = mx + b

x intercept = -b/m
y intercept = b

-b/m < b

m < -2 => m is negative so -m is positive

b/(positive #) < b

=> b is positive (otherwise if b is negative, its magnitude will increase in smaller slices, also m is not a proper fraction, so that a negative # divided by proper positive fraction will increase in magnitude)

Answer - C
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Re: DS Coordinate Geom [#permalink]

15 Apr 2011, 21:03

If the answer is A, I can explain.
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Re: DS Coordinate Geom [#permalink] 15 Apr 2011, 21:03

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In the xy-plane, if line k has negative slope, is the

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