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The y intercept of a line L is 4. If the slope of L is negative which
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Balvinder
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The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  12 Nov 2007, 19:40
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The y intercept of a line L is 4. If the slope of L is negative, which of the following could be the x intercept of L.

I. -1
II. 0
III. 6

A. I only
B. II only
C. III only
D. I and II
E. I and III
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BrentGMATPrepNow
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The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  Updated on: 03 Jul 2020, 07:06
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Balvinder wrote:
The y intercept of a line L is 4. If the slope of L is negative, which of the following could be the x intercept of L.

I. -1
II. 0
III. 6

A. I only
B. II only
C. III only
D. I and II
E. I and III


Let's draw a bunch of lines with a negative slope AND have a y-intercept of 4 (ie, passes through the point (0,4))
We get:
Image

As we can see, the x-intercept can have ANY POSITIVE value.
So, the x-intercept COULD be 6, but it could NOT be -1 or 0

Answer: C
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Originally posted by BrentGMATPrepNow on 26 Aug 2016, 11:41.
Last edited by BrentGMATPrepNow on 03 Jul 2020, 07:06, edited 1 time in total.
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jbs
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  12 Nov 2007, 19:50
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C) III only

The y-intercept is 4. Therefore we have y=mx+4

It is given that the slope is negative. Therefore the line must go from top left to bottom right.

i.e: the x-intercept has to be positive. That itself rules out I & II.

If you choose to go with the options directly, here's an approach.

y=mx+4. For the x-intercept, y=0.
i.e. mx+4=0.

We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+4 =0 would never be satisfied.

If x=6, we have 6m+4=0. A value of m=-2/3 would satisfy this equation.

Hope this helps.
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GK_Gmat
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  12 Nov 2007, 20:29
Balvinder wrote:
The y intercept of a line L is 4. If the slope of L is negative, which of the fillowing could be the x intercept of L.
I -1
II 0
III 6

A) I only
B) II only
C) III only
D) I and II
E) I and III


The stem tells us that the line is downward sloping (from left to right) and intercepts the y-axis at 4. Therefore, the all possible points of intersection on the x-axis will be positive. III is the only positive option. Answer C.
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pmenon
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  13 Nov 2007, 04:44
said C, 3 only....got it down to x=4/m ... looked at the answers and only 6 fit.
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  11 Jun 2010, 07:11
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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 a line L is 4. If the slope of L is negative which [#permalink] New post  17 Jul 2010, 10:55
Slope of the line x/a + y/b = 1 is -b/a here b = 4

hence slope = -4/a since -4/a is -ve, 'a' must be non zero and positive.
Only solution is 6

Thus C
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#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 a line L is 4. If the slope of L is negative which [#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 a line L is 4. If the slope of L is negative which [#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 a line L is 4. If the slope of L is negative which [#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 a line L is 4. If the slope of L is negative which [#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)
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  22 Jul 2014, 19:44
slope(Intercept form) = - y(intercept)/ x (intercept)
we are also given that slope should be negative.
we are told that "y intercept of a line L is 4".

s = -4/x;

x has to be positive to maintain a negative slope .

only option C satisfies.
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  22 Jul 2014, 23:16
Balvinder wrote:
The y intercept of a line L is 4. If the slope of L is negative, which of the fillowing could be the x intercept of L.
I -1
II 0
III 6

A) I only
B) II only
C) III only
D) I and II
E) I and III


With a Y-intercept of (0,4) and a negative slope, there is NO WAY for the x intercept to be less than or equal to 0

Answer is C
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  24 Jul 2014, 21:06
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Balvinder wrote:
The y intercept of a line L is 4. If the slope of L is negative, which of the following could be the x intercept of L.

I. -1
II. 0
III. 6

A. I only
B. II only
C. III only
D. I and II
E. I and III


Slope of a line = – (y intercept)/(x intercept)
Since slope is given to be negative, and y intercept is positive, we can say that x intercept must be positive too. So x intercept can be only III.

Answer (C)

For more on the slope formula, check:
http://www.veritasprep.com/blog/2011/09 ... -vertices/
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink] New post  09 Oct 2020, 05:46
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Equation of line: y = mx + c

c = 4 and m = slope is negative [consider it to be perfect negative correlation and hence m = -1]

=> y = -x + 4

=> x = 4 - y

'x' intercept when y = 0 is 4.

So, possible answer choices of (-1) and (0) are not possible.

Answer C
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Re: The y intercept of a line L is 4. If the slope of L is negative which [#permalink]
09 Oct 2020, 05:46
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