Line L passes through point (1,4), and the product of its

Question

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Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?


A. (2,3) 
B. (5,7) 
C. (4,2) 
D. (4,-1) 
E. (5, -1)

chuckle · Answer

B (5,7)
We can deduce from the conditions in the question that slope of the line > 0. From there onwards, it is POE.

bewakoof · Answer

I do understand that B leads to a positive slope.. but what I dont understand is why we need a positive slope?? because the product of the intecepts is negative?

chuckle · Answer

Yes... 
Let us take the equation of the line to be y = mx + c. (We do not know the nature of the numbers yet).
x-intercept (when y = 0) = -c/m
y-intercept (when x = 0) = c
Product of intercepts = -(c^2)/m < 0 as per the question.
=> m < 0 since c^2 is always positive.
Hope this helps.

giddi77 · Answer

Going by your logic, Only C has -ve slope (= -2/3). So C should be the answer.

chuckle · Answer

Sorry giddi...
I made a mistake. m should be > 0. 
Also, all the answer choices except B give negative slope...

giddi77 · Answer

Thanks! I also missed the -ve sign :twisted:

And no need for sorry pal. Your solution is really neat :beer

vivek123 · Answer

Yes, indeed very neat solution

My approach to this problem was slightly different. I visualized the line

, if product of y intercept & x intercept is < 0, it means the line cuts the in such a way that the slope is > 0. Only (5,7) satisfies the requirement!

kook44 · Answer

Correct me if I am wrong, but shouldn't the question be worded:
"Which of the following points  could be  on the line L?"

Good question, nonetheless. Where is it from?

likar · Answer

It's obvious when you make a drawing. Line L can be only in the direction of red lines (y+, x- or y-, x+). The only point that meets the criteria is point B ... green line is line L.

Gmate · Answer

general eqn of the line:
x/a+y/b=1.
m = -a/b
we have ab < 0.
so m>0,

therefore, angle made at the x axis is acute.
only (B) does that.

Thanks,

bewakoof · Answer

i got this question from some other forum.. I dont remember, from where..

Line L passes through point (1,4), and the product of its

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