Parallel lines have the same slope.
The slope the given line is 3, so any parallel line to this one will also have a slope of 3.
We just need to find the y-intercept of the parallel line. We can do the by plugging in the point that we want the parallel line to go through.
4 = 3 (3) + C => C = -5
Therefore the equation of the line through point (3,4) which is parallel to y = 3x + 2, is:
y = 3x - 5