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

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02 Sep 2010, 12:52
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62% (01:46) correct 38% (02:07) wrong based on 448 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).
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26 Mar 2012, 14:15
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26 Mar 2012, 13:56
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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 have a doubt in stmnt (2). K intersects the line with equation y=2(x)+3 at point (2,7) means for the line y=2(x)+3 slope is 2,but with this we cannot able to find slope of the line K. is my reasoning is right. please explain
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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.

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26 Mar 2012, 14:14
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Quote:
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 have a doubt in stmnt (2). K intersects the line with equation y=2(x)+3 at point (2,7) means for the line y=2(x)+3 slope is 2,but with this we cannot able to find slope of the line K. is my reasoning is right. please explain

My 2 cents:

Questions is asking you what is the value of M

so

1) Since k and this line with slope (1-m) are parallel

then m = 1 - m or m = 1/2

thus it is sufficient

2) we know that the point 2, 7 is on the line line y = mx + b

so 7 = 2m + b

But we know nothing else so we cannot solve for m thus it is insufficient
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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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If Line k in the xy-plane has equation y = mx + b, where m  [#permalink]

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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.

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

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29 Mar 2019, 23:05
1
Hi

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

Attachment:

1.jpg [ 20.17 KiB | Viewed 2510 times ]

Attachment:

2.PNG [ 18.18 KiB | Viewed 2516 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.

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Joined: 21 Jul 2018
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Re: If Line k in the xy-plane has equation y = mx + b, where m  [#permalink]

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30 Mar 2019, 00:19
gmatbusters wrote:
Hi

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

Attachment:
1.jpg

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.

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.
_________________
______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere and help me to learn
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Joined: 12 Jun 2019
Posts: 2
Re: If Line k in the xy-plane has equation y = mx + b, where m  [#permalink]

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29 Jul 2019, 22:11
Parallel lines have same slopes buddy

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Re: If Line k in the xy-plane has equation y = mx + b, where m   [#permalink] 29 Jul 2019, 22:11
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