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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

1

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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.

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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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.

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)

Answer is A.

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.

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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