A membership to the local gym costs $32 per month and has a registration fee of $55 . Write an equation that represents the cost (y) based upon the number of months (x) then you will calculate the cost for a membership lasting 12 months.

The equation is:

y = 32x + 55

For a membership lasting 12 months:
y = 32(12) + 55
y = 384 + 55
y = 439

Therefore, the cost for a 12-month membership is $439.