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Manager  Joined: 20 Mar 2005
Posts: 155
The y intercept of a line L is 4. If the slope of L is  [#permalink]

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11 00:00

Difficulty:   25% (medium)

Question Stats: 71% (01:10) correct 29% (01:27) wrong based on 324 sessions

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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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Joined: 12 Sep 2015
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Location: Canada
Re: The y intercept of a line L is 4. If the slope of L is  [#permalink]

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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: 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:

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Manager  Joined: 25 Jul 2007
Posts: 101
Re: The y intercept of a line L is 4. If the slope of L is  [#permalink]

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1
4
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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Director  Joined: 09 Aug 2006
Posts: 671
Re: The y intercept of a line L is 4. If the slope of L is  [#permalink]

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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 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.
VP  Joined: 28 Dec 2005
Posts: 1367
Re: The y intercept of a line L is 4. If the slope of L is  [#permalink]

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said C, 3 only....got it down to x=4/m ... looked at the answers and only 6 fit.
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Re: Need help in Coordinate geometry  [#permalink]

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1
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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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: DS:Coordinate Geometry  [#permalink]

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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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Intern  Joined: 15 May 2012
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Re: The y intercept of line l is 4. If the slope of line l is  [#permalink]

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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]

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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.
Manager  Joined: 26 Dec 2011
Posts: 91
Re: The y intercept of line l is 4. If the slope of line l is  [#permalink]

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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.
Intern  Joined: 22 Jun 2012
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GMAT 1: 730 Q49 V40 Re: The y intercept of line l is 4. If the slope of line l is  [#permalink]

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1
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.
Intern  Joined: 22 Jun 2012
Posts: 49
GMAT 1: 730 Q49 V40 Re: The y intercept of line l is 4. If the slope of line l is  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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 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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Location: Pune, India
Re: The y intercept of a line L is 4. If the slope of L is  [#permalink]

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1
4
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  [#permalink]

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_________________ Re: The y intercept of a line L is 4. If the slope of L is   [#permalink] 04 Aug 2019, 12:13
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