The y intercept of a line L is 4. if the

[agha79]

HI -
I am unable to find this question on the form. I got this question during second GMAT prep exam.

The Y intercept of a line l is 4. If the slope of l is negative, which of the following could be the X intercept of l?
I. -1
II. 0
III. 6

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

I really have no idea where to even begin to start solving this problem. I always have problem with lines problems.
OA: C (III Only)

[george.kourdin]

agha79,

when you see a problem that involes x;y intercepts/graphing, think X;Y coordinate system. draw the coordinate system, the y-axis and the x-axis and label whichever information that was given to you in the premise.

in this case we are given y intercept of 4. that means that the line intercepts the y axis at 4. mark that as a point on your graph - point (0;4). next, we are told that the slope, m, is negative. this means that the line is downward sloping (positive slope is upward sloping). we have two conditions a point and the direction of the slope. draw a line on your coordiante system. literary any line that satisfies those conditions. this line absolutly must have a positive x intercept.

if you still do not see what that is true, you may benefit from going over the underlying concepts behind the coordinate plane. read what each quadrant means, how to calculate the slope etc.

btw: if you don't see that (C) is the right answer. try drawing a line that has a y intercept of 4 and an x intercept of either -1 or 0 with a negative slope.....IT IS UNPOSSIBLE

[RonPurewal]

agha79,

when you see a problem that involes x;y intercepts/graphing, think X;Y coordinate system. draw the coordinate system, the y-axis and the x-axis and label whichever information that was given to you in the premise.

in this case we are given y intercept of 4. that means that the line intercepts the y axis at 4. mark that as a point on your graph - point (0;4). next, we are told that the slope, m, is negative. this means that the line is downward sloping (positive slope is upward sloping). we have two conditions a point and the direction of the slope. draw a line on your coordiante system. literary any line that satisfies those conditions. this line absolutly must have a positive x intercept.

if you still do not see what that is true, you may benefit from going over the underlying concepts behind the coordinate plane. read what each quadrant means, how to calculate the slope etc.

btw: if you don't see that (C) is the right answer. try drawing a line that has a y intercept of 4 and an x intercept of either -1 or 0 with a negative slope.....IT IS UNPOSSIBLE

fantastic explanation -- i have nothing to add, really, other than to remark that "unpossible" isn't a word (the correct word is impossible).

nicely done.

[george.kourdin]

lol thats an an internet slang/joke...i was trying to be clever

[RonPurewal]

lol thats an an internet slang/joke...i was trying to be clever

ah ok. i admit that i don't use computers for a single minute longer than i must.

also -- you probably know this, but a forum that is half dedicated to english sentence correction is probably the wrong place for slang that consists of incorrect english. |:

[rachelhong2012]

I love george.kourdin's approach. Mine is algebraic approach

y=mx + b

given the info, I rephrase that equation as follow:

y= (-#) x + 4 where -# means negative number/slope

x intercept is the x value you get when you set y equal to 0

I. -1
II. 0
III. 6

now let's examine all three possibilities:

0 = (-#) (-1) + 4
is that possible?
no, because (-#) (-1) = positive number, it will not cancel out with 4 to get you 0 for y, hence we cross out I

II. 0
0 = (-#) (0) + 4
is that possible?
no, because (-#) (0) gets you 0, and 0+4 equals 4, not 0 for y, hence we cross out II

finally,
III. 6
0 = (-#) (6) + 4
is that possible?
yes, that (-#) will be a negative fraction multiply by 6 to get you -4 to cancel out with 4 to equal 0 for y, hence we keep III

[RonPurewal]

rachel, nice. that works as well.

remember -- diversify your portfolio! the more methods of solution, the better.

[ShafiullahA918]

Hi Ron,

I have a question regarding the term 'intercept'.

When we say an intercept of 4 on y axis, shouldn't it mean that the line could be something like ?
a) y=mx+4 , or
b) y=mx-4

Since, the intercept means 'the length' or 'the distance from origin to the point of intersection of the line and y axis' which is the absolute value only. That is how we have always dealt with the term 'intercept' in India. I am not sure about the convention which is used internationally.

Do we need to take the negative value only if it is specifically mentioned during GMAT exam?

Thanks in advance.
-Shafi

[tim]

Standard use of "intercept" is that if b is the y-intercept of a line, that means the line goes through the point (0,b) - and, by extension, it is an absolute (no pun intended) certainty that the line does NOT go through (0,-b). This is not just the "international" use of the term; it is the ONLY use that makes sense. Despite having lived in India myself, I've never heard of an interpretation of "intercept" that takes the absolute value; to do so would strip away vital information from the problem and be pretty useless.

[RonPurewal]

Since, the intercept means 'the length' or 'the distance from origin to the point of intersection of the line and y axis' which is the absolute value only. That is how we have always dealt with the term 'intercept' in India. I am not sure about the convention which is used internationally.

i've had lots and lots and lots of students from india, and i've yet to encounter this definition of 'intercept'.

and besides—even if this were accepted as the definition somewhere, it would be a terribly inconvenient definition.
specifically, if this were the definition, then how could we actually express an 'intercept' whose sign is known? it seems this would be impossible.

[RonPurewal]

more generally, this whole thing reminds me of when people say this:
"Where I come from, '√' can mean either the positive root or the negative root."
...well, no.
no, it can't.

remember:
IN GENERAL, symbols and terms are not ambiguous.
if they were, they would have no reason to exist!