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# If Line k in the xy-plane has equation y = mx + b, where m and b are

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Manager
Joined: 02 Oct 2009
Posts: 79
If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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Updated on: 22 Dec 2017, 05:45
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Difficulty:

55% (hard)

Question Stats:

66% (01:18) correct 34% (01:20) wrong based on 327 sessions

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If Line k in the 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)

I think it is A...
from 1st ..since two lines are parallel....
m = 1- m
m =1/2

from 2nd line passes through 2,3
3 = 2 m + b..can't say ..

So answer should be A...throw some lights...

Regards,
Rohit

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-line-k-in ... 29682.html

Originally posted by KocharRohit on 17 Nov 2009, 19:53.
Last edited by Bunuel on 22 Dec 2017, 05:45, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 11 Oct 2009
Posts: 11
Re: If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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06 Jan 2010, 20:24
I'm looking at and have a bit of a problem with data sufficiency question 94, of page 281 of the 12th edition of the official GMAT review where it says:

If line k in the 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

Apparently the answer says that statement (1) alone is sufficient because the slope of line k and the other line are the same since the two lines are parallel, and thus m= 1 - m, and therefore m= 1/2.

I understand that the two lines will have the same slope since they're parralell, but does no one else see the impossibility of setting m = 1-m ??

If m is a constant or variable, it cannot possibly equal 1 minus itself, no?
That's like saying 5 = 1 - 5.
Manager
Joined: 04 Feb 2007
Posts: 77
Re: If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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06 Jan 2010, 23:09
glender wrote:
I'm looking at and have a bit of a problem with data sufficiency question 94, of page 281 of the 12th edition of the official GMAT review where it says:

If line k in the 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

Apparently the answer says that statement (1) alone is sufficient because the slope of line k and the other line are the same since the two lines are parallel, and thus m= 1 - m, and therefore m= 1/2.

I understand that the two lines will have the same slope since they're parralell, but does no one else see the impossibility of setting m = 1-m ??

If m is a constant or variable, it cannot possibly equal 1 minus itself, no?
That's like saying 5 = 1 - 5.

m = 1 -m

add m to both sides: 2m = 1
divide by 2 to both sides: m = 1/2

the equation holds only for 1/2, not any value. Plug in 1/2 into the equation and you see it holds true.
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Intern
Joined: 11 Nov 2009
Posts: 1
Re: If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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07 Jan 2010, 04:35
Hi Glender,
If two lines are parallel then each of the two lines cut the x axis at same angle.
Hence we can say that slopes will be equal.

Form the above given two equations we can take the slopes of those lines
and equate them.
therefore
m = 1-m --> 2m = 1--> m = 1/2

So we can conclude that statement1 is sufficient.

Regards,
AVR.
Director
Joined: 13 Mar 2017
Posts: 697
Location: India
Concentration: General Management, Entrepreneurship
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WE: Engineering (Energy and Utilities)
Re: If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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08 Aug 2017, 00:07
1
KocharRohit wrote:
If Line k in the 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)

I think it is A...
from 1st ..since two lines are parallel....
m = 1- m
m =1/2

from 2nd line passes through 2,3
3 = 2 m + b..can't say ..

So answer should be A...throw some lights...

Regards,
Rohit

Given a line k equation of which is y = mx+b , m and b are constants.
DS : Slope m

Statement 1: k is parallel to the line with equation y = (1-m)x + b +1.

So slope of both lines are equal. i.e. m = 1-m -> m =1/2

SUFFICIENT

Statement 2: k intersects the line with equation y = 2x + 3 at the point (2, 7)
So, (2,7 ) lies on the line y = mx+b
-> 7 = 2m+b
But from this we can't find m as there are two variable and we are not able to figure out any other way to find m.

NOT SUFFICIENT

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Joined: 02 Sep 2009
Posts: 52294
Re: If Line k in the xy-plane has equation y = mx + b, where m and b are  [#permalink]

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22 Dec 2017, 05:45
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

$$y=mx+b$$ is called point-intercept form of equation of a line. Where: $$m$$ is the slope of the line; $$b$$ is the y-intercept of the line; $$x$$ is the independent variable of the function $$y$$.

So we are asked to find the value of $$m$$.

(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is $$1-m$$, so $$1-m=m$$ --> $$m=\frac{1}{2}$$. Sufficient.

(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> $$7=2m+b$$ --> can not solve for $$m$$. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-line-k-in ... 29682.html
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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are &nbs [#permalink] 22 Dec 2017, 05:45
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# If Line k in the xy-plane has equation y = mx + b, where m and b are

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