The standard form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept. Parallel lines have the same slope, but different y-intercepts.
Since the original equation y=3x+4 has a slope of 3, use this as the slope for the new equation.
Now substitute the point (3,10) in for x and y, and solve for b.
So the equation for the line parallel to y=3x+4 that contains (3,10) is y=3x+1.