SOLUTION: Calculate m and n on these lines knowing that the line r passes through the point (1,4) and that r and s form an angle of 45 � r:mx - 2y + 5 = 0 s:nx + 6y

SOLUTION: Calculate m and n on these lines knowing that the line r passes through the point (1,4) and that r and s form an angle of 45 � r:mx - 2y + 5 = 0 s:nx + 6y - 8 = 0

Question 1071851: Calculate m and n on these lines knowing that the line r passes through the point (1,4) and that r and s form an angle of 45 �
r:mx - 2y + 5 = 0
s:nx + 6y - 8 = 0
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Putting r and s in standard form, we have:
r: y = (m/2)x + 5/2; slope=m/2 and y-intercept=5/2
s: y = (-n/6)x + 8/6; slope=-n/6 and y-intercept=8/6
Since r goes through (1,4), we can use these values to solve for m:
4 = (m/2)*1 + 5/2 -> m = 3 -> slope of r = 3/2
The angle between two intersecting lines is determined from
tan(A) = (m1-m2)/(1+m1m2). Since the angle is 45 deg and m1=3/2, we have
1 = (3/2-m2)/(1+(3/2)m2). Solving for m2 gives m2=1/5.
Thus 1/5 = -n/6, or n = -6/5
The equations for the two lines in standard form are
y = (3/2)x + 5/2 and y = (1/5)x + 4/3
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