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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What is the y-intercept?
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sudhir3127
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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...
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
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we know that b^2 = 3ac.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...
bt how did u get this b^2 = 3*3*1 ??
we only know the value of -c/a right ??
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pepeprepa
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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.
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
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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..CITI29 wrote:how can slope be -b/a?...it shld be -a/b, in which case ans shld be 'E'sudhir3127 wrote:IMO C.
for an ax+ by+ c
and slope will be -b/a
...
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manjithmanohar
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for the coordinate geometry problem,
even after considering the 2 statements there would be 2 options left.. Try drawing a graph..
thanks
even after considering the 2 statements there would be 2 options left.. Try drawing a graph..
thanks
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.
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.
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)
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
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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.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
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.
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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.
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
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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?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).
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ogbeni
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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
Based on that fact (that both statements seemed to be the same), I chose E
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crackgmat007
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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.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)
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
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
