How do you write an equation of a line perpendicular to another

Let me do it in a better color. Algebraic manipulation.

Now I need a point through which to put my perpendicular line. Add eight to negative five. If your preference differs, then use whatever method you like best. So its slope, the negative inverse of two-fifths, the inverse of two-fifths is five.

Y minus this Y value which has to be on the line. Then I flip and change the sign. You can use the Mathway widget below to practice finding a parallel line through a given point.