Ideally, you would name the route:
http://guides.rubyonrails.org/routing.html#naming-routes
And then you can refer to the route by that name.
eg. if you had:
match "tutor_appointments/new_appt" => "tutor_appointments#new_appt", as: 'new_appointment'
Then you could do:
link_to 'New Appointments', new_appointment_path
However, in this case it sounds like what you actually want is resource routing:
http://guides.rubyonrails.org/routing.html#resources-on-the-web
And you want a 'new' action for your 'tutor_appointments' resource.