The line perpendicular would be y= -1/4x +b where b is a constant.
To find the slope of the perpendicular line, take the original slope and find the negative reciprocal. That means take 1 and divide it by the slope. For example the reciprocal of 5 is 1/5 and the reciprocal of 3/5 is 5/3. After finding the reciprocal, switch the sign of the slope. If it was positive, make it negative; if it was negative make it positive. So in this case, the negative reciprocal of 4 (the original slope) is -1/4 (the perpendicular slope).
There are infinite lines perpendicular to y= 4x-3 because the y intercept doesn't matter; only the slope matters. b or , in other words, the y intercept, can be any number, positive or negative, because perpendicular refers to the angle (90 degrees) the two lines intersect, not where they intersect. For example, the two lines y= -1/4x + 100 and y= -1/4x -55 both are perpendicular lines to the original line of y= 4x-3 because their slopes make a 90 degree angle with the original equation. Their only difference is that they intersect the line at different points.