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

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If Line k in the xy-plane has equation y = mx + b, where m [#permalink] New post 26 Mar 2012, 12:56
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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
[Reveal] Spoiler: OA
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Re: coordinate geometry [#permalink] New post 26 Mar 2012, 13:14
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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Re: coordinate geometry [#permalink] New post 26 Mar 2012, 13:15
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TomB 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 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


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 [#permalink] New post 26 Mar 2012, 13:20
hai

my question is the line with equation y=2(x)+3.

x,y are coordinates on the number line. x,y coordinates are (2,7)
2= slope
3= y-intercept.

we already given the slope of the line which line K intersects but no further info about line K , so we cant find the slope of the line K. I s this correct
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Re: If Line k in the xy-plane has equation y = mx + b, where m [#permalink] New post 26 Mar 2012, 13:27
You got it .. We dont have enough info to solve for the slope of line k
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Re: If Line k in the xy-plane has equation y = mx + b, where m [#permalink] New post 31 Mar 2012, 09:34
IMO A...

parallel line means equal slope. hence m=1-m
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Re: Coordinate Geometry 2 [#permalink] New post 06 Jun 2012, 23:54
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 [#permalink] New post 01 Apr 2014, 10:30
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Re: If Line k in the xy-plane has equation y = mx + b, where m   [#permalink] 01 Apr 2014, 10:30
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