Where on the line x - y = 8 does the perpendicular from (2, 1) intersect.

From the given
line equation: x-y=8, express it in slope-intercept form (y=mx+b).

x-y
=8

  +y   +y

---------------

x     =
 8+y

   -8   -8 

----------------

x -8
=y            Or y = 1x-8 where slope  

Note that perpendicular
lines follows

Then

Determine the other line equation using and that will pass through point
(2,1).

Plug-in the values in y=mx+b

                     
       1 = (-1)(2)+b

                              1= -2 +b

                              +2  +2

                             
------------------

                              3 =b

Line
equation:  y=-1x+3 or x+y =3  based from and b =3

the two lines are
x-y=8 and x+y =3.

Applying elimination method to solve for x. 

         x-y=8           Add the to equations.

    +  x+y
=3

      -------------

        2x   = 11        Cancels
out y's since -y+y = 0.

                  Divide both sides by 2
to isolate x.

       

To solve for y, subtract
the equations as:

        x -y = 8          Or            x -y =8

-     ( x +y =3)  ------->  +  (-x -y = -3 ).    Subtraction rules of
signs. 

   -----------------            

           -2y =
5

                 Divide both sides by -2 to isolate
y.

               

Intersection point:  
(11/2, - 5/2)

This is the same as (5.5, -2.5)