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

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17 Nov 2009, 19:53
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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)

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2015, 08:12, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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

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18 Nov 2009, 02:35
Rohit, I agree that the answer to this problem is A. Statement two is not sufficient to determining the slope.

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

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18 Nov 2009, 03:09
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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

Perfectly valid reasoning.
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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.

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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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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.

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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, 19:23
Thanks guys for your responses. I now see the reasoning behind it... lapse in pretty basic logic.

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

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14 Jan 2010, 11:36
Hi guys

a quick doubt. Isnt the slope of two lines at their intersection points equal?

In that case k=2 at (2,7)

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

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15 Jan 2010, 00:38
not convincing. the equation for a line needs to be in the "y=mx+c" form for the multiplier of x to be considered as the slope. whats your take on it?

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

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15 Jan 2010, 08:14
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I agree, statement 2 gives us the value of 2 variables but we have
y=mx+b, for which we need the value of
The equation of the line y = 2x + 3 gives us no new information apart from the fact that the slope !=2.

A is the right choice.
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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are [#permalink]

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15 Jan 2010, 14:18
I agree too statement B is enough. is the OA different?

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

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15 Jan 2010, 19:23
zaarathelab wrote:
Hi guys

a quick doubt. Isnt the slope of two lines at their intersection points equal?

In that case k=2 at (2,7)

To my knowledge the slope of two intersecting (straight) lines is never equal. Now for every higher power function it can be the case.
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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are [#permalink]

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13 Feb 2016, 20:10
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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are [#permalink]

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13 Feb 2016, 20:26
zaarathelab wrote:
Hi guys

a quick doubt. Isnt the slope of two lines at their intersection points equal?

In that case k=2 at (2,7)

Although this is a pretty old thread/post, I wondered the same question and therefore sharing what I understood after researching a bit.

Slope is constant for a line but always between at least two points. Therefore in case of intersection, although the intersection point is same, the steepness (rise/run) for each line defines its slope, and hence it cannot be calculated using just one point.

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

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13 Feb 2016, 20:32
Dienekes wrote:
zaarathelab wrote:
Hi guys

a quick doubt. Isnt the slope of two lines at their intersection points equal?

In that case k=2 at (2,7)

Although this is a pretty old thread/post, I wondered the same question and therefore sharing what I understood after researching a bit.

Slope is constant for a line but always between at least two points. Therefore in case of intersection, although the intersection point is same, the steepness (rise/run) for each line defines its slope, and hence it cannot be calculated using just one point.

Slope is a fixed angle value between any two points. As such it is not defined for 1 point as you will end up getting
Slope = vertical distance / horizontal distance = 0/0

Thus it does not make any sense to talk about slope of a single point.

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

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22 May 2017, 20:40
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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are [#permalink]

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28 May 2017, 10:53
If statement 2 had said perpendicularly intersects - then the answer would have been D. Correct?

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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
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BOOKMARKED
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)

[Reveal] Spoiler:
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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Re: If Line k in the xy-plane has equation y = mx + b, where m and b are   [#permalink] 08 Aug 2017, 00:07
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