I’m a very (old) experienced driver, and I drive on the motorways every day. My slip-road tips:
1, Accelerate to 60mph on the slip road. This is the speed at which traffic in lane 1 generally travels. Don’t drive slower than 60 unless you see evidence that the traffic in lane 1 is moving slower than normal.
2, Depending on your car’s performance, don’t change into top gear yet. A lower gear will give you better acceleration if you need it.
3, Signal your intentions clearly to other road users well before you change lanes.
4, Check over your right shoulder to ensure you are aware of any vehicles in your blind spot.
5, identify a suitable gap in the traffic in lane 1 and adjust your speed as necessary to position yourself before you change lanes.
6, Making sure you have signalled before you move, do one last check of your mirrors and over your shoulder, then move decisively into the traffic and onto the motorway.
Easy! 