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In the xy-plane, what is the y-intercept of line l?

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In the xy-plane, what is the y-intercept of line l? [#permalink]

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In the xy-plane, what is the y-intercept of line l?

(1) The slope of line l is 3 times its y-intercept
(2) The x-intercept of line l is -1/3
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Re: GMATPrep: y-intercept [#permalink]

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testprep2010 wrote:
Source: GMATPrep

Please solve this question (with explanation):

In the xy-plane, what is the y-intercept of line l?
1. The slope of line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

[Reveal] Spoiler:
Ans E


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 \(x=0\)); \(x\) is the independent variable of the function \(y\).

The question is \(b=?\)

(1) The slope of line l is 3 times its y-intercept --> \(m=3b\). Not sufficient to calculate \(b\).

(2) The x-intercept of line l is -1/3 --> x-intercept is the value of \(x\) for \(y=0\) --> \(0=-\frac{1}{3}m+b\) --> \(m=3b\). Same info as above. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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uzzy12 wrote:
In the xy-plane, what is the y-intercept of line l?

(1) The slope of line l is 3 itmes the y-intercept
(2) The x-intercept of line l is -1/3


My attempt:

Line equation - y = mx +c

We need the value of c which the y-intercept of the line.

Statement 1: Slope is 3 times the y intercept.

Hence dy/dx = 3c. or m = 3c or c = m/3. Without m we cannot identify the value of c. Insufficient.

Statement 2: X intercept of the line is -1/3.

X intercept => 0 = m*x+c
0 = m (-1/3) + c
c = (1/3) * m. Without m, we cannot determine c. Insufficient.

Combining both (1) and (2), we know m = 3c and c = (1/3)m and both are the same.

No way to identify c. Hence insufficient. Answer E.
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Re: What is the y-intercept of the line [#permalink]

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To find: y-intercept of the line. When the line intercepts the y axis, x=0. Hence the original equation y=mx+c becomes y=c. Question asks for the value of c.
Statement 1: Slope of the line is 3 times the y intercept. Hence m = 3c. Insufficient.

Statement 2: The x intercept is -1/3. x intercept means y is zero. Hence the original line equation becomes
0=m(-1/3) +c

m = 3c. Same as the first equation. Insufficient.

Combining both yields nothing. Hence the answer is E.
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Re: What is the y-intercept of the line [#permalink]

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New post 18 Sep 2010, 16:09
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\(y=mx+c\)
m --> Slope
c --> Y-int

This may be re-written as :
\(\frac{x}{-c/m} + \frac{y}{c} = 1\)

We know that in terms of intercept the equation of the line is :
\(\frac{x}{X-Int} + \frac{y}{Y-Int} = 1\)

So \(X-Int = -c/m, Y-Int = c\)

(1)m=3c ... Not enough to say what the value of c is

(2)-c/m = -1/3 .... Hence m=3c. We know this is not sufficient

(1)+(2) : Same as (1) or (2)

Hence, answer is {e} ...neither statement enough
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Re: Coordinate geometry [#permalink]

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New post 08 Jan 2012, 03:11
Let the eqn of line be y=mx+c
To get y-intercept x=0 i.e. y=c ?

1) m = 3c Insuff.

2) 0 = - m/3 + c or c= m/3 Insuff. (Same as stmt 1)

Hence E

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Re: Coordinate geometry [#permalink]

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New post 08 Jan 2012, 18:57
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Rephrase: y = mx+c, c=?

1. m=3c. y=3cx+c, insuff
2. 0=-1/3m+c, c= m/3. insuff.

Both equations unsolvable. insuff. E
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 09 Dec 2012, 18:32
I approached this problem as:
y = mx + c.....equation of line... (1)

to find C

1) m = 3c.... (2)

substitute (2) in (1)

y = 3cx + c
y = c(3x +1)...... (3)

2) X intercept = -1/3

2 implies the line passes through (-1/3,0)
doesnt give enough info for M

Combined
substitute point (-1/3,0) in (3)

0 = c(3 * -1/3 +1)
0 = c (-1+1 )
c = 0 ?

what did i do wrong ?

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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 10 Dec 2012, 01:41
uroopesh wrote:
I approached this problem as:
y = mx + c.....equation of line... (1)

to find C

1) m = 3c.... (2)

substitute (2) in (1)

y = 3cx + c
y = c(3x +1)...... (3)

2) X intercept = -1/3

2 implies the line passes through (-1/3,0)
doesnt give enough info for M

Combined
substitute point (-1/3,0) in (3)

0 = c(3 * -1/3 +1)
0 = c (-1+1 )
c = 0 ?

what did i do wrong ?


From 0=c(-1+1) --> 0=c*0, which holds true for ANY value of c not only for c=0. Also, notice that if c=0, then m=0, thus our line is y=0 which contradicts the statements.

Hope it's clear.
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 30 Sep 2013, 12:35
testprep2010 wrote:
In the xy-plane, what is the y-intercept of line l?

(1) The slope of line l is 3 times its y-intercept
(2) The x-intercept of line l is -1/3


1. y=mx+c

given >> m=3c

y=3cx+c

when y=0, x=-1/3 .. from point -1/3,0 we can draw 2 lines satisfying the condition given above, one with obtuse angle(-ve y intercept) and other with acute angle(+ve y intercept) .. hence, not sufficient

2. x=-1/3
we can draw infinite lines passing from this point .. very clear ..
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Re: GMATPrep: y-intercept [#permalink]

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New post 31 Mar 2014, 23:31
Bunuel wrote:
testprep2010 wrote:
Source: GMATPrep

Please solve this question (with explanation):

In the xy-plane, what is the y-intercept of line l?
1. The slope of line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

[Reveal] Spoiler:
Ans E


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 \(x=0\)); \(x\) is the independent variable of the function \(y\).

The question is \(b=?\)

(1) The slope of line l is 3 times its y-intercept --> \(m=3b\). Not sufficient to calculate \(b\).

(2) The x-intercept of line l is -1/3 --> x-intercept is the value of \(x\) for \(y=0\) --> \(0=-\frac{1}{3}m+b\) --> \(m=3b\). Same info as above. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.


Hi Bunuel,

In every DS question, if both statements provide the exact same insufficient information and that information is derived in different ways ( slope in (1) and x-intercept in (2) ) , can we assume that both together are insufficient?

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Re: GMATPrep: y-intercept [#permalink]

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New post 01 Apr 2014, 00:01
TooLong150 wrote:
Bunuel wrote:
testprep2010 wrote:
Source: GMATPrep

Please solve this question (with explanation):

In the xy-plane, what is the y-intercept of line l?
1. The slope of line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

[Reveal] Spoiler:
Ans E


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 \(x=0\)); \(x\) is the independent variable of the function \(y\).

The question is \(b=?\)

(1) The slope of line l is 3 times its y-intercept --> \(m=3b\). Not sufficient to calculate \(b\).

(2) The x-intercept of line l is -1/3 --> x-intercept is the value of \(x\) for \(y=0\) --> \(0=-\frac{1}{3}m+b\) --> \(m=3b\). Same info as above. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.


Hi Bunuel,

In every DS question, if both statements provide the exact same insufficient information and that information is derived in different ways ( slope in (1) and x-intercept in (2) ) , can we assume that both together are insufficient?



Hi Toolong150,

Do not assume anything on DS question unless and until it is obvious.

To your above question, If you get same insufficient information from both statements then ans is E as is above the case. If you look at the above question,actually both statement tell you the same thing but in st1 it talks about slope and st 2 it talks about x intercept

St 1 y= mx+ c says m =3c now if you find x intercept (y=0) we get 0=3cx+c or x=-1/3

Same as st 2


Hope it helps
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 30 Nov 2014, 15:47
Bunuel wrote:
testprep2010 wrote:
Source: GMATPrep

Please solve this question (with explanation):

In the xy-plane, what is the y-intercept of line l?
1. The slope of line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

[Reveal] Spoiler:
Ans E


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 \(x=0\)); \(x\) is the independent variable of the function \(y\).

The question is \(b=?\)

(1) The slope of line l is 3 times its y-intercept --> \(m=3b\). Not sufficient to calculate \(b\).

(2) The x-intercept of line l is -1/3 --> x-intercept is the value of \(x\) for \(y=0\) --> \(0=-\frac{1}{3}m+b\) --> \(m=3b\). Same info as above. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.


Hi Bunuel,

I realize that "b' is the y intercept in the equation y = mx + b.

-That being said, I was a little confused as to whether I should solve for B or solve for Y by equation x to 0. If I did the latter, i would get y = b.

-How do I know I I should plug in values for X and Y or solve for B? This part seems to give me the most trouble.

Thanks

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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 01 Dec 2014, 05:39
russ9 wrote:
Bunuel wrote:
testprep2010 wrote:
Source: GMATPrep

Please solve this question (with explanation):

In the xy-plane, what is the y-intercept of line l?
1. The slope of line l is 3 times its y-intercept
2. The x-intercept of line l is -1/3

[Reveal] Spoiler:
Ans E


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 \(x=0\)); \(x\) is the independent variable of the function \(y\).

The question is \(b=?\)

(1) The slope of line l is 3 times its y-intercept --> \(m=3b\). Not sufficient to calculate \(b\).

(2) The x-intercept of line l is -1/3 --> x-intercept is the value of \(x\) for \(y=0\) --> \(0=-\frac{1}{3}m+b\) --> \(m=3b\). Same info as above. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.


Hi Bunuel,

I realize that "b' is the y intercept in the equation y = mx + b.

-That being said, I was a little confused as to whether I should solve for B or solve for Y by equation x to 0. If I did the latter, i would get y = b.

-How do I know I I should plug in values for X and Y or solve for B? This part seems to give me the most trouble.

Thanks


y = b cannot be sufficient. When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Hope it's clear.
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 20 Feb 2016, 02:29
Bunuel: can you suggest similar questions? Thanks

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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 22 Feb 2016, 01:18
Nina1987 wrote:
Bunuel: can you suggest similar questions? Thanks


Check our question bank: viewforumtags.php

DS questions on coordinate geometry: search.php?search_id=tag&tag_id=41
PS questions on coordinate geometry: search.php?search_id=tag&tag_id=62

Hope it helps.
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 24 Jul 2016, 14:22
Isn't C true because the equation is y = 3x + 1? Making the y intercept 1. I don't see how it can be any other equation..

I don't see any other equation that will satisfy both of those statements?

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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 24 Jul 2016, 22:08
alpham wrote:
Isn't C true because the equation is y = 3x + 1? Making the y intercept 1. I don't see how it can be any other equation..

I don't see any other equation that will satisfy both of those statements?


y = 3b*x + b substitute b to get the equations.
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 01 Feb 2017, 17:12
If the slope and y-intercept of a line in xy plane are m and c respectively, then the line can be represented by the equation y = mx + c and the x=intercept of the line will be -c/m

Statement 1: m = 3c ---> Not sufficient

Statement 2: -c/m = -1/3 ---> m = 3c ---> Not sufficient

1 & 2 Together: We have no new information ---> Not sufficient

hence E
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Re: In the xy-plane, what is the y-intercept of line l? [#permalink]

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New post 06 May 2017, 12:23
stunn3r wrote:
testprep2010 wrote:
In the xy-plane, what is the y-intercept of line l?

(1) The slope of line l is 3 times its y-intercept
(2) The x-intercept of line l is -1/3


1. y=mx+c

given >> m=3c

y=3cx+c

when y=0, x=-1/3 .. from point -1/3,0 we can draw 2 lines satisfying the condition given above, one with obtuse angle(-ve y intercept) and other with acute angle(+ve y intercept) .. hence, not sufficient

2. x=-1/3
we can draw infinite lines passing from this point .. very clear ..

Can you elaborate on your reasoning for 2). Not any line would suffice, would it? The line would still have to have m=3c.

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Re: In the xy-plane, what is the y-intercept of line l?   [#permalink] 06 May 2017, 12:23

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