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Question 87791: Write the equation of the line L satisfying the given geometric conditions. For Problems 36 and 40, refer to Example 5 (p 631) for the solution of similar problems. Recall that parallel lines have identical slopes – they only differ in their y-intercept – fLor Problem 36.
Answer by malakumar_kos@yahoo.com(315)   (Show Source):
You can put this solution on YOUR website!
Problem 40 requires that you find the slope of the line that is perpendicular to the one represented by the given equation.
L has y-intercept (0, 2) and is perpendicular to the line with equation:
2x – 3y = 6.
L is the line for which we have to find the eq'n and given L is perpendicular
to 2x-3y = 6, and has intercept (0,2)
Let the eq'n to L be Y=mx+c therefore 2 = m.0 +c or c = 2
to find the slope of the line 2x-3y = 6 ; -3y = -2x+6 ; y = 2x/3+6/-3
y = 2x/3-2 ; therefore slope m =2/3
the slope of line L = -3/2 (the lines are perpendicular hence product of thier slopes = -1,, M.m = -1, M = -1/2/3 = -3/2)
the eq'n to the line L is y = -3x/2+2 (by substituting for M & c from the above) or eq'n can be reduced to 2y = -3x+4 OR 3x+2y = 4
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