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GMATFocus Q3 - Coordinate Geometry

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by frizo » Wed Feb 11, 2009 10:24 pm
If Line K in th xy-plane has equation y=mx+b, where m and b are constants, what is the slope of k?

1) K is parallel to the line with equation y = (1-m)x + b + 1
2) K intersects the line with equation y=2x+3 at the point (2,7))

A
Last edited by frizo on Thu Feb 12, 2009 8:05 am, edited 1 time in total.
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Source: — Data Sufficiency |
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Re: GMATFocus Q3 - Coordinate Geometry

by x2suresh » Wed Feb 11, 2009 10:40 pm
frizo wrote:If Line K in th xy-plane has equation y=mx+b, where m and b are constants, what is the slope of k?

1) K is parallel to the line with equation y = (1-x)x + b + 1
2) K intersects the line with equation y=2x+3 at the point (2,7))

A

y = (1-x)x + b + 1
--> is not a line.. looks lit it is parabola.. Please check the question again.
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by frizo » Thu Feb 12, 2009 8:06 am
Sorry, it is y = (1-m)x + b + 1
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by BuckeyeT » Thu Feb 12, 2009 8:26 am
(1) If K is parallel to another line, they share the same slope. Since (1) states the line y=(1-m)x + b + 1, it is of the form y = mx + b (where m=slope, b=y-intercept). So, we know the slope is (1-m) and the intercept is (b + 1) where m and b are constants. Since we can state the answer as a constant value (slope of k = (1-m)), the statement is sufficient.

(2) This statement gives us the intercept of the two lines and the slope of 1 line. The other line can have a variety of slopes other than the slope given and still intersect at (2,7) - try drawing a line on paper, pick a point on that paper, and see how many lines you can draw through that line. This statement is insufficient.

So, A.
Last edited by BuckeyeT on Thu Feb 12, 2009 8:27 am, edited 1 time in total.
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by bluementor » Thu Feb 12, 2009 8:27 am
If two straight lines are parallel, then they have the same slopes.

Statement 1: Lines y=mx+b and y=(1-m)x+b+1 are parallel, therefore:

m = 1-m
m=0.5 , Sufficient.

Statement 2: A line that intersects y=2x+3 at (2,7) can have any slope, therefore insufficient.

Choose A.

-BM-
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by bhumika.k.shah » Tue Feb 09, 2010 10:01 am
This looks simple :) But what about that +1 in the equation y=(1-m)x+b+1

Are we to ignore that ? if so, then why ? If we consider it , then the answer would change.


bluementor wrote:If two straight lines are parallel, then they have the same slopes.

Statement 1: Lines y=mx+b and y=(1-m)x+b+1 are parallel, therefore:

m = 1-m
m=0.5 , Sufficient.

Statement 2: A line that intersects y=2x+3 at (2,7) can have any slope, therefore insufficient.

Choose A.

-BM-
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by stufigol » Tue Feb 09, 2010 11:03 am
you don t have to consider it...
it is like y= (1-m)x+ D with D=b+1
U just need to consider that they are parallel not the distance between the two...if u change D they ll still be // but the distance will change
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