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

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If Line K in the xy-plane has equation y=mx+b, where m and b [#permalink] New post 20 May 2004, 23:55
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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)

this is a DS question

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Re: question 5 [#permalink] New post 21 May 2004, 05:28
carsen 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)

this is a DS question

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A.

slopes are identical when lines are parallel. in this case slope is (1-m)
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Re: question 5 [#permalink] New post 21 May 2004, 06:01
carsen 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)

this is a DS question

Regards


I think it can be solved only by 1
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 [#permalink] New post 21 May 2004, 13:47
The answer is A

By definition, parallel lines have the same slope, no matter what the intercept is. So your only looking at the "m" part of the y=mx+b.

Therefore, according to statement (1), y=(1-m)x+b+1 has the same slope as y=mx+b. Which means that 1-m = m...m=1/2

Statement 2 gives you no information about the slope except that it is not equal to 2.
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 [#permalink] New post 21 May 2004, 13:56
I think the question is asking us to determine the value of m
not whether slope is 1-m

In that case the answer is E.
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 [#permalink] New post 21 May 2004, 17:18
Agree... I took the question to mean that they want the numerical value of the slope. I choose E.
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 [#permalink] New post 21 May 2004, 17:25
It is A.

1. Parallel lines have same slope, or inclination to any reference line.
m = 1-m, or m = (1/2) = the slope of K
2. it says K and y = 2x+3 are not parellel. Hence, the angle b/w these two lines is any but 0, 180, and 360 degrees. Insufficient.
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 [#permalink] New post 21 May 2004, 20:39
Thanks for all the replies guys

The official answer is A.

I need to study more about these slopes. Which book would give some insights, shortcuts, tips on such slope questions ... Kaplan, OG or anyother? I have no idea on questions like slope and unable to understand the above explainations.

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 [#permalink] New post 21 May 2004, 22:27
anandnk wrote:
I think the question is asking us to determine the value of m
not whether slope is 1-m

In that case the answer is E.


In my post above you will see that stataement (1) shows that m-1 = m.

1-m=m
1 = 2m
m = 1/2
  [#permalink] 21 May 2004, 22:27
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