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)

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.

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. |:

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

rachel, nice. that works as well.

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