Important fact: The slopes of perpendicular lines are negative reciprocals of one another. Thus, if the given line here has the slope 1/4, the slope of any line perpendicular to it will be -4 (the negative reciprocal of 1/4).
(0,2) is the y intercept of the new line.
Thus, the new line's equation is y = mx + b, or y = -4x + 2.