PreCalculus
posted by Alexis .
Write Parametric equations of 3x+1/2y=2

we know x =rcosØ and y = rsinØ
3rcosØ + (1/2)rsinØ = 2
6rcosØ + rsinØ = 2
r(sinØ  6cosØ) = 2
or
r = 2/(sinØ  6cosØ)
looks good:
http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx++6cosx%29 
Reiny gave you good polar coordinates, but if all you want is parametric equations, try
x = t/3
y = 1 + t/2
or
x = (2+t)/3
y = 2t