parallel to the line y=4x+1, and that passes through points (2,3).

What seems to be the trouble?

If lines are parallel, then the slopes are the same. You are given the slope, m.

Just use your x and y values in y=mx+b to find b and you're done.

parallel to the line y=4x+1, and that passes through points (2,3).
Actually, it is very very simple.

All lines parallel to the given are: y = 4x + K

This passes through (2, 3): 3 = 8 + k
So k = -5

Hence: y = 4x -5