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# In the xy-plane, if line k has a negative slope and passes

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Intern
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In the xy-plane, if line k has a negative slope and passes [#permalink]

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06 Jun 2012, 23:04
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Difficulty:

65% (hard)

Question Stats:

51% (00:37) correct 49% (01:11) wrong based on 49 sessions

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In the xy-plane, if line k has negative slope and passes through the point (−5,r ), is the x-intercept of line k positive?

(1) The slope of line k is –5.
(2) r > 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-xy-plane-if-line-k-has-negative-slope-and-passes-135197.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 May 2013, 03:12, edited 2 times in total.
Edited the question and the OA.

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Intern
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Re: Coordinate Geometry 3 [#permalink]

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07 Jun 2012, 01:04
Statement-1

With slope of -5
If r>25, then x-intercept is positive, otherwise negative.
So, statement-1 is not sufficient.

Statement-2

With r>0
x-intercept can be either negative or positive depending on the slope and value of r

Even combining both the statements no additional info can be obtained

Ans:E

PS: Hello Val1986, how did u get A as the answer?? Correct me if I did any mistake in the above explanation.

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Kellogg MMM ThreadMaster
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Re: Coordinate Geometry 3 [#permalink]

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07 Jun 2012, 01:38
Hi,

For a line passing through (-5,r) with negative slope there can be many lines.

Even after using (1) or (2), we can say the x-intercept would be positive or not.

Answer should be (E).
Attachments

lines.jpg [ 7.45 KiB | Viewed 2437 times ]

Last edited by cyberjadugar on 07 Jun 2012, 05:01, edited 1 time in total.

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Re: Coordinate Geometry 3 [#permalink]

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07 Jun 2012, 02:56
cyberjadugar wrote:
Hi,

For a line passing through (-5,r) with negative slope there can be many lines.

Even after using (1) or (2), we can say the x-intercept would be positive or not.

Answer should be (E).

I have the same reasoning.
The answer should be E

OR am I missing something!

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Intern
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Re: Coordinate Geometry 3 [#permalink]

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07 Jun 2012, 10:16
Answer should be E

statement 1

r = 25+c

for C to be positive r should be > 25 , is it clear as per statement 1 .

Statement 2 :

r is positive , this is also not enough to find out value of C as r might fall 0<r<25 for this values C is -VE

comibining two statements also we dont have perfect solution

So, definitely should be E

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Math Expert
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Re: In the xy-plane, if line k has a negative slope and passes [#permalink]

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07 Jun 2012, 10:41
Val1986 wrote:
In the xy-plane, if line k has negative slope and passes through the point (−5,r ), is the x-intercept of line k positive?

(1) The slope of line k is –5.
(2) r > 0

The answer to this question is E, not A. OA edited.

In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?

This question can be done with graphic approach (just by drawing the lines) or with algebraic approach.

Algebraic approach:

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line, $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$), and $$x$$ is the independent variable of the function $$y$$.

We are told that slope of line $$k$$ is negative ($$m<0$$) and it passes through the point (-5,r): $$y=mx+b$$ --> $$r=-5m+b$$.

Question: is x-intercept of line $$k$$ positive? x-intercep is the value of $$x$$ for $$y=0$$ --> $$0=mx+b$$ --> is $$x=-\frac{b}{m}>0$$? As we know that $$m<0$$, then the question basically becomes: is $$b>0$$?.

(1) The slope of line $$k$$ is -5 --> $$m=-5<0$$. We've already known that slope was negative and there is no info about $$b$$, hence this statement is insufficient.

(2) $$r>0$$ --> $$r=-5m+b>0$$ --> $$b>5m=some \ negative \ number$$, as $$m<0$$ we have that $$b$$ is more than some negative number ($$5m$$), hence insufficient, to say whether $$b>0$$.

(1)+(2) From (1) $$m=-5$$ and from (2) $$r=-5m+b>0$$ --> $$r=-5m+b=25+b>0$$ --> $$b>-25$$. Not sufficient to say whether $$b>0$$.

Answer: E.
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Re: In the xy-plane, if line k has a negative slope and passes [#permalink]

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07 Jun 2012, 10:46
In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?

(1) The slope of line k is -5
(2) r>0

Graphic approach:

If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

When we take both statement together all we know is that slope is negative and that it crosses some point in II quadrant (-5, r>0) (this info is redundant as we know that if the slope of the line is negative, the line WILL intersect quadrants II). Basically we just know that the slope is negative - that's all. We can not say whether x-intercept is positive or negative from this info.

Below are two graphs with positive and negative x-intercepts. Statements that the slope=-5 and that the line crosses (-5, r>0) are satisfied.

$$y=-5x+5$$:
Attachment:

1.png [ 9.73 KiB | Viewed 2413 times ]

$$y=-5x-20$$:
Attachment:

2.png [ 10.17 KiB | Viewed 2409 times ]

More on this please check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In the xy-plane, if line k has a negative slope and passes [#permalink]

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07 Jun 2012, 16:54
Sorry guys apparently the question had a mistake in my answer key! Thanks a lot guys!

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Re: In the xy-plane, if line k has a negative slope and passes   [#permalink] 07 Jun 2012, 16:54
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# In the xy-plane, if line k has a negative slope and passes

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