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

Question

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 gmat_ds_prep.JPG

Bunuel · Accepted Answer

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.

ezhilkumarank · Answer

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.

ezhilkumarank · Answer

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.

shrouded1 · Answer

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

himym · Answer

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 ?

Bunuel · Answer

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.

russ9 · Answer

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

Bunuel · Answer

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.

GMATYoda · Answer

IMG_2761.JPG

CrackverbalGMAT · Answer

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

Equation of a line in point intercept form is y=mx+c, where m is the slope of the line and c is the y-intercept of the line.
Y intercept is the point where line crosses the Y axis. i.e. x=0 at that point

(1) The slope of line l is 3 times its y-intercept
 
 m= 3c
 y = 3cx +c
Statement 1 alone is not sufficient to find the value of c.

(2) The x-intercept of line l is -1/3

X intercept is the point where line crosses the X axis. i.e. y=0 at that point .
0= m(-1/3) + c
c = m/3
m=3c 
i.e . The slope of line l is 3 times its y-intercept, which is same as the info given in Statement 1.
hence, insufficient.

Even if you combine statement 1 and 2, it's not sufficient to answer the question as both the statements say the same thing.

Option E is the answer.

Thanks,
  Clifin J Francis,
GMAT SME

tanishagarg19 · Answer

reply-
0= c (-1+1)
0= c (0)
0= 0
Hence, the variable c gets nullified. we cannot find the value of c, as any number multiplied with 0 will give us a zero.

jaykayes · Answer

The relationship between the slope and the intercepts of a straight line is that slope = y-intercept/x-intercept

To find y-intercept, we need to know the   values   of the slope   and   the x-intercept.

Statement 1 doesn’t tell us anything about the x-intercept.
Further, it only gives us the   ratio   of slope to y-intercept, but it doesn’t give us the value of the either.
Insufficient.

Statement 2 gives us the value of the x-intercept, but doesn’t give us the value of the slope.
Insufficient.

Combined, we don’t get any new information – we still don’t know the value of the slope.
Insufficient.

Correct answer: E

nosaj · Answer

I got this question wrong and very much agree that  jaykayes . That it is important to realise that the ACTUAL value of the slope is what is required to get to the answer here. Given neither statements give us the ACTUAL value of the slope (m). The answer is E.

In addition, I also made an error and interpreted x-intercept -1/3 as x = -b/m - I realise that this is wrong because -1/3 is the x-coordinate and doesn't represent the slope nor the y-intercept.

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

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