how do you find the equation of a line perpendicular to another line at a point?

The gradient of the perpendicular line is the negative reciprocal of the gradient of the original line. For example if the gradient of the original line is 4, the gradient of the perpendicular line is -1/4. If the gradient of the original line is 1/2 , the gradient of the perpendicular line is -2 (=-2/1). The equation of the perpendicular line can then be found by substituting the gradient (m) and the given point (x,y) into the equation y=mx+c.(the reciprocal of a number is 1/that number)