What is the equation of the line passing through 3 1 and is parallel to 3x plus 5y equals 6 showing work?

If: 3x+5y = 6

Then: y = -3/5x+6/5 which means it has a slope of -3/5

Parallel equation: y-1 = -3/5(x-3) => 5y-5 = -3(x-3) => 5y = -3x+14

Or as: 3x+5y = 14