Write an equation of a line that is perpendicular to x=3 and passes through (0,-4)

The equation of a vertical line: x = a (a - any real number).

The line perpendicular to x = 3 is a horizontal line.

The equation of horizontal line: y = b (b - any real number).

The horizontal line passes through (0, - 4) → x = 0 and y = - 4.

Therefore your answer is

y = - 4