Question 1071851
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