I have a line and an arc which are tangential to each other. How can I use a number slider to distribute a set of points evenly across both?

In other words, if the amount of points I want turns out to have a distance of, say 1 meter, and in order to make it even across both curves, one point may fall 0.7 meters from the end of the first curve, and 0.3 meters from the start of the second…

Hmm… the output is “2 locally defined values”, instead of a single one… and the “point on curve” node gives me 2 points instead of 1… so I guess it didn’t work?

Yes for CurveJoin to work the curves have to coincide in their end points.
To achieve this you could split them with their intersection and join their reminder.