Where your boat is at each point of the course is crucial in our sport. You don't just have a course of about 20 gates. You have 3 imaginary gates between each gate to make sure you stay on line. Where you are between gates is crucial. If you are on line, you will likely be very clean and fast. You lose a lot of time by being off-line.
I see a lot of boaters going down the course off-line, but acting like they don't know they are off-line. The top guys will be on line. But I sometimes tell younger boaters to use the lines that the senior boaters or the women use, more conservative lines because the younger boaters often don't have the strength to pull off the more direct moves that the top men use. So, there are different lines for different people. You need to learn to be obsessive-compulsive about being on line. And the bigger and faster the water, the more important it is to be on line. On easier water, you can make up some time just by paddling faster, but on bigger water, it is crucial to be on line.
So, what is the correct line? The general rule is that if the next gate is a downstream, you need to be angled towards that gate is the standard rule. But this is incorrect. You need to be angled towards a point upstream of the next gate. That way, you can turn before the next gate and be angled towards the gate after it.
However, there is an exception to the general rule that you should be angled across towards the next gate as you go through a downstream gate. If the downstream gate is in an eddy, you normally just go straight through it and then turn towards the next gate. This may seem counter-intuitive, but there is no worry about slipping downstream if the gate is in an eddy and you can just do a pivot and then head towards the next gate.
If the next gate after a down is an upstream, you don't have to be angled towards it. You need to figure out the best approach for the next up and get on that line as soon as possible. On artificial courses, you often want to be headed mostly downstream towards an upstream gate, without too much cross-stream angle. On natural rivers, you usually want to be going across as you approach an upstream gate.
In the case of double upstream gates, you usually want to take a very direct line between the 2 upstreams. A lot of boaters make the mistake of losing time by going up high out of the first upstream instead of going directly across the next upstream gate.
And another place where boaters sometimes lose time is on the exit of upstreams. Unless you have to ferry out of the up for the next gate, it is crucial to get the boat moving downstream towards the next gate as soon as possible. Many boaters waste time by doing a great entry to an upstream and lose time by going a long ways up on the exit. Get the boat moving downstream as soon as possible after an up, unless you have to ferry across for the next gate.
Apply these general rules for slalom lines and you will have a good run. Break them and you will pay for it in lost time, penalties and lost energy fighting against the water. Good boaters use the water to their advantage and keep the boat on line and moving as much as possible, with little loss of boat speed.