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# Line m passes through the origin. Line l is parallel to line

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Line m passes through the origin. Line l is parallel to line [#permalink]

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18 Mar 2012, 21:38
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Line m passes through the origin. Line l is parallel to line m. What are the equations of the two lines?

(1) The horizontal distance between the two lines is 5 units.

(2) Line l has a y-intercept of 2.5

Last edited by Bunuel on 19 Mar 2012, 01:07, edited 2 times in total.
Edited the question.
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18 Mar 2012, 23:50
Smita04 wrote:
Line m passes through the origin. Line l is parallel to line m. What are the equations of the two lines?

(1) The horizontal distance between the two lines is 5 units.

(2) Line l has a y-intercept of 2.5

Since the lines are parallel the slopes would be same, say m
Let the Line M be y=mx
So line L will be y=mx+c

Statement 1
Considering the horizontal distance on x axis , this distance can be taken towards +ve or -ve side of origin.
So the slopes of the lines and the value of c cannot be determined.
So insufficient.

Statement 2
Now we know the value of c but we still don't know the value of slope.
So insufficient.

From 1+2
We know that horizontal distance is 5 i.e x intercept and y intercept is 2.5 i.e c=2.5
Since the y intercept is +ve ,horizontal distance i.e x intercept is -ve.
So the line passes through (-5,0)
therefore using the equation we get
0=m(-5)+2.5
or m=1/2
So the equations are y=0.5x
and y=0.5x+2.5
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Re: Line m passes through the origin. Line l is parallel to line [#permalink]

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19 Mar 2012, 01:06
Line m passes through the origin. Line l is parallel to line m. What are the equations of the two lines?

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line and $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$).

From the stem:
Since parallel lines have the same slope, then the slopes of l and m are the same;
Since a line passing through the origin has y-intercept equal to zero then the equation of line m would be $$y_m=mx$$ and the equation of line l would be $$y_l=mx+b$$

(1) The horizontal distance between the two lines is 5 units --> basically we are told that the x-intercept of line l is either -5 or 5, so we know that line l passes either through the point (-5, 0) or (5, 0). Not sufficient.

(2) Line l has a y-intercept of 2.5 --> $$b=2.5$$, so we know that line l passes through the point (0, 2.5). One point is not enough to determine (fix) a line. Not sufficient.

(1)+(2) Now, even take together we cannot determine whether line l passes through the point (-5, 0) or (5, 0). So, we would have two possible points of line l: (-5, 0) and (0, 2.5) OR (5, 0) and (0, 2.5), which means that we would have two possible equations of line l and m: $$y_l=0.5*x+2.5$$ and $$y_m=0.5*x$$ OR $$y_l=-0.5*x+2.5$$ and $$y_m=-0.5*x$$. Not sufficient.

To demonstrate.
Case 1:
Attachment:

Case 1.png [ 7.73 KiB | Viewed 5186 times ]

Case 2:
Attachment:

Case 2.png [ 8.08 KiB | Viewed 5179 times ]

For more on this subject please check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: Line m passes through the origin. Line l is parallel to line [#permalink]

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19 Mar 2012, 01:45
Thanx Bunuel
there is lot to learn from you...
I will not delete my post so that others could learn from my mistake.
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Re: Line m passes through the origin. Line l is parallel to line [#permalink]

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19 Mar 2012, 08:03
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Re: Line m passes through the origin. Line l is parallel to line [#permalink]

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27 Jun 2013, 22:30
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

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Re: Line m passes through the origin. Line l is parallel to line [#permalink]

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25 May 2015, 03:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Line m passes through the origin. Line l is parallel to line   [#permalink] 25 May 2015, 03:44
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