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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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udaymathapati
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If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  02 Sep 2010, 12:52
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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).
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Bunuel
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  02 Sep 2010, 13:19
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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?

\(y=mx+b\) 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.

Answer: A.
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  26 Mar 2012, 14:15
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For Coordinate Geometry check:

24. Coordinate Geometry



For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  07 Jun 2012, 00:54
For line K, y=mx+b implies slope=m

From Statement-1,

As slopes of parallel lines are equal, m = (1-m)

m=1/2
Statement-1 is sufficient.

From statement-2,

line K passes through (2,7)
7=2.m + b
m = (7-b)/2
Not sufficient.

Ans:A
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  29 Mar 2019, 13:51
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel 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?

\(y=mx+b\) 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.

Answer: A.
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  29 Mar 2019, 23:05
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Hi

I couldd not get your query, the principle is as below:



Show Spoiler
Attachment:
1.jpg
1.jpg [ 20.17 KiB | Viewed 27424 times ]

Show Spoiler
Attachment:
2.PNG
2.PNG [ 18.18 KiB | Viewed 27439 times ]


Gmatprep550 wrote:
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel 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?

\(y=mx+b\) 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.

Answer: A.

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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  30 Mar 2019, 00:19
gmatbusters wrote:
Hi

I couldd not get your query, the principle is as below:



Show Spoiler
Attachment:
1.jpg

Show Spoiler
Attachment:
2.PNG


Gmatprep550 wrote:
Hi chetan2u, VeritasKarishma, Bunuel, amanvermagmat, gmatbusters,

I did not understood the bold part in below question, can any please assist.

Bunuel 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?

\(y=mx+b\) 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.

Answer: A.


Hi gmatbusters

Apologies for not highlighting proper issue,

I was not able to get following part.


slope of this line is 1−m1−m, so 1−m=m1−m=m

Even if slope is m then also how 1-m = m? I feel that "m" mentioned in equation is different.
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  29 Jul 2019, 22:11
Parallel lines have same slopes buddy

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If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  24 Sep 2020, 04:52
Bunuel 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?

\(y=mx+b\) 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.

Answer: A.



HiBunuel

for st 1 after equating equations i am getting 1 = 2mx-x

(1-m)x + b +1 = mx+b

or x-mx+b+1 = mx+b

1 = mx+b-x+mx-b

1= 2mx-x

what am i doing wrong :?
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Mahi14
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  29 Sep 2020, 09:27
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For statement 2, can we use m1*m2 =-1 for intersecting lines?

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adkor95
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  29 Oct 2020, 10:31
Bunuel 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?

\(y=mx+b\) 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.

Answer: A.


Thanks! But is this implying that no matter the format of the equation, the term/number multiplying the x-value is the gradient? I was thrown off by '+ 1' in the equation.
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Re: If line k in the xy-plane has equation y = mx + b, where m and b are [#permalink] New post  24 Jan 2023, 03:44
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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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