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

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.

\(y=mx+c\)
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

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.

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.

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

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.

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

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.