How do you write an equation for a perpendicular line?

To write an equation for a perpendicular line, first determine the slope of the original line. If the slope of the original line is ( m ), the slope of the perpendicular line will be the negative reciprocal, ( -\frac{1}{m} ). Using the point-slope form ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is a point on the new line, substitute the perpendicular slope and point to derive the equation of the perpendicular line. Finally, you can rearrange it into slope-intercept form, ( y = mx + b ), if desired.