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The y intercept of line l is 4. If the slope of line l is

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The y intercept of line l is 4. If the slope of line l is [#permalink] New post 11 Jun 2010, 06:52
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A
B
C
D
E

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79% (01:51) correct 21% (01:11) wrong based on 56 sessions
The y intercept of line l is 4. If the slope of line l is negative ,which of the following could be the x intercept of line l?

I) -1
II) 0
III) 6

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
[Reveal] Spoiler: OA
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Re: Need help in Coordinate geometry [#permalink] New post 11 Jun 2010, 07:11
C

equation of a line y = mx+c.
If y intercept of line l is 4, then one of the points is (0,4) - by making x zero.

We know that the slope 'm' is negative. To find the x intercept of the line, make y zero in the above line equation. We get x = -c/m.
Since the value of c is 4 and the slope is negative. x has to be positive, and not negative or 0.
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Re: The y intercept of line l is 4. If the slope of line l is [#permalink] New post 22 Jul 2012, 18:48
Hi Bunuel,
I am not convinced with the answer for the above question. Let me tell you how I approached it. The equation is y=mx+4, where 4 is the y-intercept (given) and since it has got a negative slope, the equation becomes, y=(-m)x+4. Now, to determine x-intercept, we consider y=0, then, -mx+4=0, hence mx=4 and since m has to be negative (it is given that slope is negative for the line), I chose x=-1, so that m=-4. According to the above calculations, I get the answer as A. But the answer is C. Please help me get the concept right.
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Re: The y intercept of line l is 4. If the slope of line l is [#permalink] New post 22 Jul 2012, 19:12
Try visualizing the problem.

There are 2 givens:
1) The y intercept is 4
2) The slope is negative

Now draw out a coordinate plane and try to draw a few sample solutions that meet the above givens.

The only way the line can cross -1 is if the slope was positive. The line will also never cross 0 because that would form an undefined slope.

Solution 1) 6 is the only valid option. Therefore, the correct answer is C.
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Re: The y intercept of line l is 4. If the slope of line l is [#permalink] New post 23 Jul 2012, 00:47
The answer is C. If the slope is negative of the line then either it passes through the 1 st quadrant <starting from II towards IV> or passes through the third quadrant <starting from II towards IV>.. Thus, the intercepts are either both positive or both negative. Given in the question, its a positive intercept, the other one will be a positive as well. Thus, 6.
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Re: The y intercept of line l is 4. If the slope of line l is [#permalink] New post 23 Jul 2012, 02:16
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sharmila79 wrote:
Hi Bunuel,
I am not convinced with the answer for the above question. Let me tell you how I approached it. The equation is y=mx+4, where 4 is the y-intercept (given) and since it has got a negative slope, the equation becomes, y=(-m)x+4. Now, to determine x-intercept, we consider y=0, then, -mx+4=0, hence mx=4 and since m has to be negative (it is given that slope is negative for the line), I chose x=-1, so that m=-4. According to the above calculations, I get the answer as A. But the answer is C. Please help me get the concept right.

No. You are mixing it up.
the slope is negative
Hence you can write
y=(-m)x+4
since -m is negative, in this case m must be positive
again your slope is -m, not m!!

So later if you say mx=4
x is necessarily positive since m is positive.

Try to be rigorous when you create variables.
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Re: The y intercept of line l is 4. If the slope of line l is [#permalink] New post 23 Jul 2012, 02:18
Also, even though the answer is C, this problem is not very well written IMO since an infinite negative slope could cause the x intercept to be 0 :D (though "The intercept" can imply that there is only one y intercept)
Re: The y intercept of line l is 4. If the slope of line l is   [#permalink] 23 Jul 2012, 02:18
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