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Manager  Joined: 10 Feb 2010
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In the xy-plane, what is the y-intercept of line l?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 62% (01:32) correct 38% (01:24) wrong based on 1400 sessions

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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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Math Expert V
Joined: 02 Sep 2009
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Re: In the xy-plane, what is the y-intercept of line l?  [#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

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

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

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2
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: In the xy-plane, what is the y-intercept of line l?  [#permalink]

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1
$$y=mx+c$$
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: In the xy-plane, what is the y-intercept of line l?  [#permalink]

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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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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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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

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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Joined: 02 Sep 2009
Posts: 59017
Re: In the xy-plane, what is the y-intercept of line l?  [#permalink]

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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

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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Hi Bunuel ,

I stopped solving and answered C because I thought combining 1 and 2 contained 2 unique equations. But further solving shows that they both end in m=3b.

My question is, if statement 1 gave m=3b and statement 2 gave a different equation. Can the answer in that case be C since the 2 equations are distinct? Please help... Thanks. Re: In the xy-plane, what is the y-intercept of line l?   [#permalink] 16 Jul 2019, 02:20
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