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Line D passes through point (2,5), and the product of its xintercept
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Updated on: 21 Oct 2014, 14:05
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66% (02:19) correct 34% (02:23) wrong based on 162 sessions
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Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D? A. (5,10) B. (3,2) C. (1,7) D. (1,2) E. (3,1) ______________________________________________________________________________________________ Anyone can clarify the meaning of "the product of its xintercept and yintercept is positive" on the diagram for me? Thanks
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Originally posted by yvonne0923 on 12 Apr 2011, 21:43.
Last edited by Bunuel on 21 Oct 2014, 14:05, edited 1 time in total.
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Re: Line D passes through point (2,5), and the product of its xintercept
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12 Apr 2011, 22:09
If a is the Xintercept and b is the Yintercept. The line passes through the points (a,0) and (0,b) The slope of this line is (b/a) If a*b is positive, means both a & b have the same sign. Which means (b/a) is a negative number or the slope is negative. The rest of the solution is as above.
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Re: Line D passes through point (2,5), and the product of its xintercept
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12 Apr 2011, 21:53
I think this means we are looking for a line that has negative slope.
Only D satisfies that condition.
Point (2,5)
A. (5,10) m = 10  5/ 5 (2) = +ve B. (3,2) m = 25 / 3  (2) = +ve C. (1,7) m = 7  5 / 1  (2) = +ve D. (1,2) m = 2  5 / 1  (2) = ve E. (3,1) m = 1  5 / 3  (2) = +ve



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Re: Line D passes through point (2,5), and the product of its xintercept
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12 Apr 2011, 23:57
The slope of the line is ve, the only point that makes the slope ve is D. (5  2)/(2 + 1) = 3/1 Answer  D
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Re: Line D passes through point (2,5), and the product of its xintercept
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16 Apr 2011, 19:15
yvonne0923 wrote: Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D?
A. (5,10) B. (3,2) C. (1,7) D. (1,2) E. (3,1) _______________________________________________________________________________________________
Anyone can clarify the meaning of "the product of its xintercept and yintercept is positive" on the diagram for me?
Thanks First and foremost, make sure you draw quick diagrams in coordinate geometry problems. Half your problem will be solved there and then. So the line would look something like one of these lines if it passes through (2, 5). Attachment:
Ques2.jpg [ 11.85 KiB  Viewed 6562 times ]
Further, xintercept is the point on the x axis where the line intersects the x axis. y intercept is the point on the y axis where the line intersects the y axis. Say if a line passes through (1, 0), its x intercept much be 1. If a line passes through (0, 3), its y intercept must be 3. Of course, for any straight line, x and y intercepts have unique values. What is the point of giving that the product of x and y intercepts is positive? This implies that either both x and y intercept are positive or both are negative. Now look at the lines above. Would it look something like the green line or the red line? The red line has negative x intercept and positive y intercept so the product of its intercepts will be ve. Hence, it cannot be the required line. The green line has both intercepts positive so it can be our line ( it is downward sloping from left to right hence it has negative slope) Now, I have plotted the approximate position of all the points. Which one can possibly lie on this line? Attachment:
Ques3.jpg [ 10.06 KiB  Viewed 6565 times ]
I think it is quite clear that the line can only pass through (1, 2) and still maintain the negative slope. In all other cases, the line would have a positive slope i.e. it will look like the red line
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Line D passes through point (2,5), and the product of its xintercept
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03 Nov 2014, 11:29
Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D?
(A) (5,10) (B) (3,2) (C) (1,7) (D) (1,2) (E) (3,1)



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Re: Line D passes through point (2,5), and the product of its xintercept
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03 Nov 2014, 12:37
Here is how i approached the question: Equation of a line is (yy1)/(xx1)=m y1= 5 , x1 = 2 (y5)/(x+2)=m y5=mx+2m y=m(x+2)+5 If both the xintercept and yintercept are positive, if you draw the line then the slope of the line would be ve. Plug in the solutions y=m(x+2)+5, only D will give you a ve value for m, thus it's the solution , thanks !



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Re: Line D passes through point (2,5), and the product of its xintercept
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04 Nov 2014, 02:43
aashu4uiit wrote: Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D?
(A) (5,10) (B) (3,2) (C) (1,7) (D) (1,2) (E) (3,1) Merging similar topics. Please refer to the discussion above.
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Re: Line D passes through point (2,5), and the product of its xintercept
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17 Jul 2017, 10:26
VeritasPrepKarishma wrote: yvonne0923 wrote: Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D?
A. (5,10) B. (3,2) C. (1,7) D. (1,2) E. (3,1) _______________________________________________________________________________________________
Anyone can clarify the meaning of "the product of its xintercept and yintercept is positive" on the diagram for me?
Thanks First and foremost, make sure you draw quick diagrams in coordinate geometry problems. Half your problem will be solved there and then. So the line would look something like one of these lines if it passes through (2, 5). Attachment: Ques2.jpg Further, xintercept is the point on the x axis where the line intersects the x axis. y intercept is the point on the y axis where the line intersects the y axis. Say if a line passes through (1, 0), its x intercept much be 1. If a line passes through (0, 3), its y intercept must be 3. Of course, for any straight line, x and y intercepts have unique values. What is the point of giving that the product of x and y intercepts is positive? This implies that either both x and y intercept are positive or both are negative. Now look at the lines above. Would it look something like the green line or the red line? The red line has negative x intercept and positive y intercept so the product of its intercepts will be ve. Hence, it cannot be the required line. The green line has both intercepts positive so it can be our line ( it is downward sloping from left to right hence it has negative slope) Now, I have plotted the approximate position of all the points. Which one can possibly lie on this line? Attachment: Ques3.jpg I think it is quite clear that the line can only pass through (1, 2) and still maintain the negative slope. In all other cases, the line would have a positive slope i.e. it will look like the red line Thanks for the excellent explanation; Can you please update new question checking similar concept?



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Re: Line D passes through point (2,5), and the product of its xintercept
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03 Dec 2018, 06:10
yvonne0923 wrote: Line D passes through point (2,5), and the product of its xintercept and yintercept is positive. Which of the following points could be on line D?
A. (5,10) B. (3,2) C. (1,7) D. (1,2) E. (3,1)
______________________________________________________________________________________________
Anyone can clarify the meaning of "the product of its xintercept and yintercept is positive" on the diagram for me?
Thanks Since prod of X and Y intercept is postive so line passes through 1st quad or 3rd quad means slope will be negative/Now find M< 0 ..by chosing one point from option and one point as (2,5)



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Re: Line D passes through point (2,5), and the product of its xintercept
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21 Mar 2020, 04:54
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Re: Line D passes through point (2,5), and the product of its xintercept
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