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A line is graphed on a coordinate plane. How many times less is the di

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Bunuel
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A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   09 Feb 2015, 06:44
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A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

(1) The slope of the line is −9/13.

(2) The y-intercept is located at (0, 26).

Kudos for a correct solution.
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   16 Feb 2015, 05:35
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Bunuel wrote:
A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

(1) The slope of the line is −9/13.

(2) The y-intercept is located at (0, 26).

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

C. This problem is a classic "Why Are You Here?" data sufficiency problem related to Statement 2. The slope of a line (with one exception) will provide the ratio of x-intercept to y-intercept. Say that the line were in the form y = (-9/13)x + 9. The y-intercept would be 9, and the x-intercept would be 13; if you double the y-intercept just to see the ratio pattern, you'd see that the ratio stays exactly the same: y = (-9/13)x + 18 would leave a y-intercept of 18 and an x-intercept of 26, again for a ratio of y-int : x-int of 9:13.

But here is why you need to consider what statement 2 is telling you - it's clearly not sufficient on its own, but what it does tell you is that the line does not pass through the origin (0,0). If it were to pass through the origin, the ratio of intercepts would be 0:0, since the intercept points would be at exactly that (0, 0) point. That's the only point on the coordinate plane for which the ratio of x-intercept to y-intercept is not defined by the slope.
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   10 Feb 2015, 06:22
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To solve this problem we need the x and y intercepts. We can find these intercepts with the \(y = mx + b\) equation of the line.
So if we can find the line's slope (m) and the y-intercept (b), we will have sufficient information.
Each of the two statements gives us one piece of the equation, so we need to take them together. The correct answer is C.
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   10 Feb 2015, 08:01
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sterling19 wrote:
To solve this problem we need the x and y intercepts. We can find these intercepts with the \(y = mx + b\) equation of the line.
So if we can find the line's slope (m) and the y-intercept (b), we will have sufficient information.
Each of the two statements gives us one piece of the equation, so we need to take them together. The correct answer is C.


hi sterling,
i think you have answered generally all question correctly but this may be wrong although approach has been correct..
i think ans should be A.. tht is slope itself is sufficient in this case..
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   10 Feb 2015, 08:11
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ans A..
the question gives following info..
Let the y intercept be (0,y) and x intercept, (x,0)...
distance between the y intercept and x axis is y-0=y..
distance between the x intercept and y axis is x-0=x..

now the question asks us.." How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?".
It basically means (x-y)/x = 1-y/x or ( 1- slope )..
now lets take the statements..
1) statement one gives us slope... sufficient as we required slope itself
2) statement two tells us about y intercept... x intercept required.. insufficient

ans A
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   10 Feb 2015, 08:29
Here we go :

Basically, the question is asking the relationship between the x-intercept and y-intercep.

So let the equation of the line be -> y = mx +c ----(1)

St1: The slope of the line is −9/13.

m = -9/13 ->Substitute in (1)

So y = -9/13 * (x) + c

To find y-intercept, put x = 0

y = c ---(2)

To find x-intercept, put y = 0

0 = -9/13 * (x) + c

x = 13/9 * c

From (2)

x = 13/9 * y

Hence St1 is sufficient.

St2: The y-intercept is located at (0, 26).

From (1)
y = 26

and

x = -26 / m

Clearly insufficient

Option A is correct
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   10 Feb 2015, 12:48
Quote:
A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

(1) The slope of the line is −9/13.

(2) The y-intercept is located at (0, 26).

since we need to know HOW MANY TIMES LESS is the distance, we do not need to find a value for the distance, but for a number which multiplies the y intercept distance from the x-ax.

(2) does not provide us with the x intercept. insuff
(1) does provide us with the slope. if, for example the y intercept is 9, we know that the x intercept is at x=13. if the y intercept is 4,5, we know that the x intercept is at 6,5. its the sample multiple. since all parallels of THIS exact line contain the same multiple, the parallel going through 0 also has the same multiple.

so A is suff
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A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   26 Dec 2016, 13:04
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Bunuel wrote:
Bunuel wrote:


..... The slope of a line (with one exception) will provide the ratio of x-intercept to y-intercept....

... If it were to pass through the origin, the ratio of intercepts would be 0:0



Can somebody clarify the two statements above?

Firstly there is no a ratio 0:0 in the world of Maths because 0/0 cannot be defined. So something else means by 0:0.

Also for the first statement lets say that we have the line y = 2x + 10

x inter. will be derived by 2x = -10 then x = -5
y inter. will be derived by y = 10

then the ratio x:y = -5/10 = - 1/2 which is not equal to 2:1
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   27 Sep 2017, 05:50
chetan2u wrote:
ans A..
the question gives following info..
Let the y intercept be (0,y) and x intercept, (x,0)...
distance between the y intercept and x axis is y-0=y..
distance between the x intercept and y axis is x-0=x..

now the question asks us.." How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?".
It basically means (x-y)/x = 1-y/x or ( 1- slope )..
now lets take the statements..
1) statement one gives us slope... sufficient as we required slope itself
2) statement two tells us about y intercept... x intercept required.. insufficient

ans A


I am confused about the OA. Can an expert have a look at this question? I also thought the answer to be A? Thanks.
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   27 Sep 2017, 05:55
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deucebigalow wrote:
chetan2u wrote:
ans A..
the question gives following info..
Let the y intercept be (0,y) and x intercept, (x,0)...
distance between the y intercept and x axis is y-0=y..
distance between the x intercept and y axis is x-0=x..

now the question asks us.." How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?".
It basically means (x-y)/x = 1-y/x or ( 1- slope )..
now lets take the statements..
1) statement one gives us slope... sufficient as we required slope itself
2) statement two tells us about y intercept... x intercept required.. insufficient

ans A


I am confused about the OA. Can an expert have a look at this question? I also thought the answer to be A? Thanks.


Check here: https://gmatclub.com/forum/a-line-is-gr ... l#p1485415
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   02 Aug 2018, 10:40
The answer is C, not A.

There is one exception that makes Statement 1 insufficient: If the line crosses the origin, then the x- and y-intercepts are both at (0,0). Since they are at the exact same point, the distance between the y-intercept and the x-axis and the distance between the x-intercept and the y-axis are the SAME (i.e. both distances = 0).
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   16 Sep 2019, 11:16
Bunuel wrote:
Bunuel wrote:
A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

(1) The slope of the line is −9/13.

(2) The y-intercept is located at (0, 26).

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

C. This problem is a classic "Why Are You Here?" data sufficiency problem related to Statement 2. The slope of a line (with one exception) will provide the ratio of x-intercept to y-intercept. Say that the line were in the form y = (-9/13)x + 9. The y-intercept would be 9, and the x-intercept would be 13; if you double the y-intercept just to see the ratio pattern, you'd see that the ratio stays exactly the same: y = (-9/13)x + 18 would leave a y-intercept of 18 and an x-intercept of 26, again for a ratio of y-int : x-int of 9:13.

But here is why you need to consider what statement 2 is telling you - it's clearly not sufficient on its own, but what it does tell you is that the line does not pass through the origin (0,0). If it were to pass through the origin, the ratio of intercepts would be 0:0, since the intercept points would be at exactly that (0, 0) point. That's the only point on the coordinate plane for which the ratio of x-intercept to y-intercept is not defined by the slope.


Sir, can you please give an easier solution to this problem?
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   06 May 2020, 06:16
The answer should be C..What statement 2 tells us is the line does not pass through (0,0) point where the difference between Y-intercept and X-axis and X intercept and Y-axis is undefined. So we need statement 2 as well to answer the question.

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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   06 May 2020, 06:28
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GMAThunterr wrote:
The answer should be C..What statement 2 tells us is the line does not pass through (0,0) point where the difference between Y-intercept and X-axis and X intercept and Y-axis is undefined. So we need statement 2 as well to answer the question.

Posted from my mobile device


Hi GMAThunterr

The Official answer is Option C only. so you are CORRECT :) :thumbsup:

1st statement only tells us the inclination where we can't find intercepts using this statement.
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A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   17 Jul 2020, 19:53
Hi GMATinsight
may I solve the problem by using equation y=mx+b?
statement 1) y=-9/13x + b, we don't know about b, insufficient
statement 2) 26 = m*0 + b---> 26=b, but we don't know about the distance from x intercept to y-axis, so it is still insufficient

combine two statements, we have y = -9/13x + 26, sufficient
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A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   17 Jul 2020, 21:40
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Well, the Question is really easy if you are aware of the concept of Intercept and Slope
Statement1: Slope is provided as (-9/13). So lets put this in equation: y = -(9/13)*x + c
c here is the y intercept. Put x =0 , you will have Y intercept which is c. But c can be anything . Even if you put X intercept constant then also you wont be able to find the difference between Y intercept and X intercept. Hence insufficient

Statement 2: Y intercept is located at (0,26). We got a problem here. We do not know the slope and hence Line can intercept at any location in the X axis for y=0. We just know the Y intercept . Hence insufficient.

Combining Statement 1 and 2, we know the Y intercept location which is a point on the the line that will satisfy the line:
We have equation y =(-9/13)*x + c . We know c=26 , and we also know for y =0 , x = (26 *13/9).
This is sufficient to know the difference between X intercept and Y intercept.

Hence Answer should be C

Hit kudos if this makes sense to you
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Re: A line is graphed on a coordinate plane. How many times less is the di [#permalink] New post   23 Dec 2022, 04:04
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