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# 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]

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15 Apr 2011, 20:19
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85% (hard)

Question Stats:

38% (01:56) correct 62% (01:30) wrong based on 29 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-xy-plane-if-line-k-has-negative-slope-is-the-129055.html
[Reveal] Spoiler: OA

Last edited by skbjunior on 16 Apr 2011, 04:15, edited 1 time in total.
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15 Apr 2011, 21:15
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skbjunior wrote:
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. I will provide OA soon. Thanks!

(1) Not Sufficient.
Attachment:

x_intercept_less_than_y.png [ 8.46 KiB | Viewed 1560 times ]

(2)Not Sufficient.
Attachment:

slope_less_than_minus_2.png [ 8.55 KiB | Viewed 1560 times ]

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

Attachment:

combining_both.png [ 7.34 KiB | Viewed 1562 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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15 Apr 2011, 21:24
1
KUDOS
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)

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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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