Basel to lucerne using our swiss pass +sts

Greetings, our family will be arriving in Basel on may 8 via paris tgv. We have a 2 for 1 swiss pass for me and my wife and sts family card for our kids. What would be the fastest route to lucerne from basel using our swiss pass? I would like to maximize the use of our pass, I noticed on the map given to us that there is no continuous red line going from basel to lucerne. Does that mean that we have to pay extra on the train with the dotted line?

Hello Lloyd this is from sbb timetable
Basel SBB Tu, 08.05.12 dep 11:04 duration 1:01 changes 0
Luzern arr 12:05

Basel SBB Tu, 08.05.12 dep 11:17 duration 1:13 changes 0
Luzern arr 12:30

Basel SBB Tu, 08.05.12 dep 11:31 duration 1:24 changes 1 in Olten
Luzern arr 12:55

don't know what time you arrive in Basel but these trains run hourly at these times. The broken line you refer to signifies a tunnel not a mountain train requiring extra payment - those are shown as dotted lines not broken lines.
hope this helps. Maggie

Greetings Maggie,

What a sigh of relief, I thought we were going to pay extra. Thank you so much Maggie.

Lloyd