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April 11th, 2011, 03:39 AM  #1 
Newbie Joined: Apr 2011 Posts: 8 Thanks: 0  slope of line in respect to 2nd line helpppppp please
Consider two straight lines L1 (y = 2x +1) and L2 (y=x). a) What is the slope of line L1 in respect to line L2? b) What is the equation of line L1 in respect to line L2? NOTE. Think that the original xy coordinate system has been rotated in respect to the origin so that line L2 defines the new xaxis x´ and y´ is the new yaxis! this is another example i have to study for this test tomorrow havent a clue how to do this please explain thank you 
April 11th, 2011, 11:29 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,164 Thanks: 472 Math Focus: Calculus/ODEs  Re: slope of line in respect to 2nd line helpppppp please
a) Let and represent the slopes of the given lines and respectively. Using the fact that: we can find the respective slope m between the two lines by taking the difference of the angles: For this problem, we have thus: b) Using rotation of axes, where the angle of rotation is we have: and We use: In the new coordinate system, the line becomes: Thus, we find with we have the line: 

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