Given
The equation of the line is,

To find the equation of the line parallel to y=4x+1.
Step-by-step explanation:
It is given that,
The equation of the line is,

Since two parallel lines have same slope.
Then,
The slope of the line parallel to y=4x+1 is, 4.
Therefore, the equation of the line parallel to y=4x+1 is of the form,

Hence, the equation of the line parallel to y=4x+1 is c) y=4x-2.