Question 893570
As a formula?  Try this.

Given y=mx+b, find the equation of a line perpendicular to it which contains the point (u,v).


You want a line {{{y=-(1/m)x+k}}}, and to find this k, the y-intercept, solve for k.
{{{k=y-(-(1/m))x}}}
{{{k=y+(1/m)x}}}
We are accepting (u,v) as a specific, given point.


Use (u,v) to find k.
{{{k=v+(1/m)*u}}}


Using these we put together our wanted line's equation.
{{{y=-(1/m)x+(v+(1/m)u)}}}
{{{highlight(y=-(1/m)x+(v+u/m))}}}
This formula could be simplified further <i>if you want</i>:
{{{highlight(y=-(1/m)x+(vm+u)/m)}}}