Write Parametric equations of -3x+1/2y=2

Answer 1

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

Answer 2

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