What is the y-intercept?

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CappyAA: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon Jun 16, 2008 11:07 amFollowed by: 14 members; Thanked: 21 times; GMAT Score:750

by CappyAA » Tue Aug 12, 2008 5:12 pm

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)

Thanks,
Cappy

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Wed Aug 13, 2008 2:48 am

IMO C.

u need to know some basic formulae in coordinate geometry to be able to solve this question easily

here it goes..

for an ax+ by+ c

X intercept will be -c/a
y intercept will be -c/b

and slope will be -b/a

if u know these ur done ..

statement 1 says ...

for line L slope = 3 times the y intercept. using formula above we can write it as

-b/a = 3* (-c/b)

b^2 = 3ac.... insufficient........................1

statement II

X intercept is -1/3
which means

-c/a = -1/3 in sufficient .........................2

using i and 2 we know

b^2 = 3ac

b^2 = 3*3*1

hence b = +/- 3

now from this we can find the y intercept easily..

y intercept will -c/b = -1/ 3 ( from statements we know b > 0)

hope it helps...

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Vignesh.4384: Master | Next Rank: 500 Posts; Posts: 443; Joined: Sat Jun 28, 2008 6:33 pm; Thanked: 5 times

by Vignesh.4384 » Wed Aug 13, 2008 4:18 am

sudhir3127 wrote:IMO C.

u need to know some basic formulae in coordinate geometry to be able to solve this question easily

here it goes..

for an ax+ by+ c

X intercept will be -c/a
y intercept will be -c/b

and slope will be -b/a

if u know these ur done ..

statement 1 says ...

for line L slope = 3 times the y intercept. using formula above we can write it as

-b/a = 3* (-c/b)

b^2 = 3ac.... insufficient........................1

statement II

X intercept is -1/3
which means

-c/a = -1/3 in sufficient .........................2

using i and 2 we know

b^2 = 3ac

b^2 = 3*3*1

hence b = +/- 3

now from this we can find the y intercept easily..

y intercept will -c/b = -1/ 3 ( from statements we know b > 0)

hope it helps...

we know that b^2 = 3ac.

bt how did u get this b^2 = 3*3*1 ??
we only know the value of -c/a right ??

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

by CITI29 » Mon Aug 18, 2008 7:32 am

sudhir3127 wrote:IMO C.

for an ax+ by+ c

and slope will be -b/a

...

how can slope be -b/a?...it shld be -a/b, in which case ans shld be 'E'

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Mon Aug 18, 2008 7:47 am

That is not a coordinate geometry simple problem.
For me it's E because there is an infinity of possibilities. I just give you 2 to check if I am right.

y=-3x-1 the y-intercept is -1 and the slope is 3 times -1, its x-intercept is -1/3
y=3x+1 the y-intercept is 1 and the slope is 3 times 1, its x-intercept is -1/3
They both respect all the conditions... so we cannot answer the question, so E

Personally, I think coordinate geometry one may be solved by graphs.

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Mon Aug 18, 2008 8:04 am

CITI29 wrote:
sudhir3127 wrote:IMO C.

for an ax+ by+ c

and slope will be -b/a

...
how can slope be -b/a?...it shld be -a/b, in which case ans shld be 'E'

yeah CITI .. it is -a/b .. sorrie abt the mistake... i shud have recitified it .. but never came back to it... yeah I go with E as well..

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manjithmanohar: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Mar 25, 2009 4:50 am

by manjithmanohar » Wed Apr 01, 2009 7:30 am

for the coordinate geometry problem,

even after considering the 2 statements there would be 2 options left.. Try drawing a graph..

thanks

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abcdefg: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Sep 22, 2008 5:11 pm; Thanked: 1 times

by abcdefg » Sun Jul 19, 2009 7:21 am

These are the equations I have

From statement 1:
y= mx+b
y= 3bx + b
not sufficient to find b because we dont know x,y.

From statement 2:
y=mx+b
0= m(-1/3)+b
we don't know m, so we can't find b.

Combining both equations:
0= 3b(-1/3) +b
0= -b+b
0=0

Not enough, hence E. However what I don't get is, why did I get 0=0 when I combined those 2 equations? What does it mean to get 0=0? Thanks.

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qwe12: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat May 30, 2009 11:22 am; Thanked: 2 times

by qwe12 » Sun Jul 26, 2009 3:56 pm

my way of solving this is as follows, if y = mx + c, is the equation of a line, where c is the y intercept.

from 1) m = 3c

=> y = 3cx + c, to determine the y intercept, plug y = 0

0 = c(3x + 1)

Here, we can 2 options c=0 and x can be anything
or 3x+1 = 0 and c can be anything.

NOT SUFFICIENT.

from 2)

y = m(-1/3) + c
y = -m/3 + c

so c = y + m/3, if y goes to 0, c = m/3, and m can be anything,

NOT SUFFICIENT.

Using (1) and (2) we find we have 2 equations and 3 unknowns.

y = 3cx + c
y = -m/3 + c

We need 3 equations to solve for 3 unknowns.

SO (E)

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: What is the y-intercept?

by Ian Stewart » Sun Jul 26, 2009 4:56 pm

CappyAA 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)

Thanks,
Cappy

If you understand the meaning of the slope of a line, you may be able to see why the answer here is E without using any algebra. If a line has slope m, that means that if you go one unit to the right, the line rises m units. If you go across by 1/3 of a unit, the line will thus rise by m/3.

That's what's happening in the question above: the x-intercept is at -1/3. If you move 1/3 of a unit to the right, you'll be at the y-axis, and thus the y-intercept of the line, and by the definition of the slope, the line will have risen by m/3 units. That is, the y-intercept will be at (0, m/3). In other words, if Statement 2 is true, it absolutely must be true that the slope is 3 times the y-intercept, and thus Statement 1 doesn't provide us with any new information at all.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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gmat_2010: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Thu Apr 09, 2009 10:33 am

by gmat_2010 » Fri Jul 31, 2009 4:59 am

I think it is E. In any case it can't be C because condition 2 can be derived from condition 1.

Consider x intercept = a, y intercept = b
Then, equation of line is:

(x/a) + (y/b) = 1

Or, y = (-b/a)*x + b

Also, from 1:
slope is 3 times the y-intercept
Hence, (-b/a) = 3*b
Or, a = -1/3

So, C is wrong.

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

Re: What is the y-intercept?

by niraj_a » Fri Jul 31, 2009 7:31 am

Ian Stewart wrote:
If you move 1/3 of a unit to the right, you'll be at the y-axis, and thus the y-intercept of the line, and by the definition of the slope, the line will have risen by m/3 units. That is, the y-intercept will be at (0, m/3).

Ian, would we always do this to find the Y intercept of a given line i.e. move the x intercept wherever it is to the Y intercept?

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ogbeni: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Sep 02, 2006 7:50 pmFollowed by: 1 member; Thanked: 10 times

by ogbeni » Fri Jul 31, 2009 7:56 am

Is it just me but don't the 2 statements say the same thing? Didn't realize that until I tried combining both. Very interesting question

Based on that fact (that both statements seemed to be the same), I chose E

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

Re: What is the y-intercept?

by crackgmat007 » Tue Aug 11, 2009 8:11 pm

CappyAA 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)

I see from the above posts that both statements provide same info. can someone help how to get m = 3b with the details in stmt 2? tx.

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amirp: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Dec 20, 2009 2:02 pm; Thanked: 3 times

by amirp » Wed Sep 29, 2010 12:03 pm

Here is how I approached this question.

1) we can have many solutions to satisfy this (ex: y intercept can be 1 or 2 and we can still get a line that has 3 times the slope )

Eliminate: A & D

2) doesn't help at all... infinite answers

Eliminate: B

1+2) Not sufficient: you can have 2 different lines, one going in the positive and one going in the negative direction.

Eliminate: C

only E left

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