If you are trying to extend your parallel line while keeping its orientation (angle), please try following steps.
Before this, you need to make sure "Advanced Digitizing Panel" is displayed by View | Panels |(check) Advanced digitizing panel.
- Toggle Editing on your line layer
- Add Feature
- Enable advanced digitizing tools
- Click your first point
- Click your end point, then you can see a green line extends out
- Follow this green line and click at your desired point
You can also set the angle to a fixed number, and lock, in the "a" entry of the Advanced Digitizing Panel. (I do not know which way is easier for your case.)
To do this easily, setting Snapping Option is highly recommended.