The equation of the new route if it is to be perpendicular to the old route and will go through point (P, Q) is 
Since the equation of the path of the old route can be described as y = two fifthsx − 4, it is 
Now the gradient of this old route is m = 2/5.
Since the new route is perpendicular to the old route, if we let its gradient be m', then mm' = -1 (since the routes are perpendicular).
So, m' = -1/m
m' = -1/2/5
m' = -5/2
So, the gradient of the new route is m' = -5/2.
Since the new route passes through the point (P, Q), the equation of the new route passing through this point is given by
(y - Q)/(x - P) = m'.

This is the equation of the new route given in gradient form where m' is the gradient of the new route.
Since m' = -5/2,



So, the equation of the new route if it is to be perpendicular to the old route and will go through point (P, Q) is 
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