an equation of a line through (-1,4) which is perpendicular to the line y= 4x + 1 has 1/4 slope and y - intercept of

A line perpendicular  to the given one will have slope of  (-1/4)

The equation  of  this line  is

y = (-1/4)(x - - 1)  + 4

y = (-1/4)(x + 1) + 4

y = (-1/4)x  - 1/4 + 4

y = (-1/4)x +  15/4

The  y intercept  is   (15/4)