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April 11th, 2011, 03:39 AM   #1
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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 co-ordinate system has been
rotated in respect to the origin so that line L2 defines the new
x-axis x and y is the new y-axis!

this is another example i have to study for this test tomorrow havent a clue how to do this please explain thank you
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April 11th, 2011, 11:29 AM   #2
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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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