find the distance from (6,-4) to the line defined by y=2x-6

Typically we ask for the shortest distance because the distance from the line varies. So here we go... 

There is a line perpendicular to our line that passes through (6,-4). Since it is perpendicular it has the slope -1/2 

 


 

After some simplifying we can get 

 



Notice that this new line must intersect our original at a point exactly parallel to (6,-4) (why?) 

Therefore if we find the point of intersection we can use that point to find our distance 


 
and this leads us to the x-coordinate which is x=2 and so y=2(2)-6=-2 

Next we find the distance between (6,-4) and (2,-2) 


 
and this gives us 

 



Actually in precalculus there is a formula: 
 



:)