Thank you for contacting Mearto. This is a Bach 42BO trombone.
Below I have included links to asking and hammer prices for this model.
I could not find a model called 42 K on the Bach site. I did see this on trombones for sale and have listed links below. If I am misunderstanding the model, please let me know.
Yours appears to be in very good condition and I have taken this into account in my valuation.

Serial number 31042, 1977-78:
https://www.bachloyalist.com/serial-numbers-trombone/

Model info 42BO:
https://www.bachbrass.com/instruments/trombones/42bo

Bach 42K trombone asking prices:

$499, ‘poor condition’
https://reverb.com/item/1087095-vincent-bach-42k-stradivarius-bb

$1600
https://brassgurus.com/products/used-bach-42k-tenor-trombone-gold-brass-bell

$1699
https://reverb.com/item/13447257-used-bach-42k-tenor-trombone-gold-brass-bell

New $1989
https://www.guitarcenter.com/Bach/42K-Stradivarius-Professional-Trombone.gc

42BO asking prices:

$1874, ‘good’
https://bit.ly/3lcsh7Q

$2750, ‘mint’
https://bit.ly/3yj5St4

$2889, mint
https://reverb.com/item/18871637-bach-42bo-stradivarius-tenor-trombone-f-rotor-open-wrap

$2999, condition unclear
https://bit.ly/3zQKwDM

$2999, mint
https://bit.ly/3lcshVo

$3200, good
https://reverb.com/item/37125891-bach-42bo-stradivarius-series-f-attachment-trombone-with-lacquer-slide

$3399 new
https://reverb.com/p/bach-42bo-stradivarius-series-tenor-trombone-w-slash-open-wrap-f-attachment-standard-rotor-valve

Hammer prices:

$821 42BO
https://www.ebay.com/itm/393431792432?hash=item5b9a5cbb30:g:8sYAAOSwQMVg050p

$860 42BO
https://www.ebay.com/itm/114794446702?hash=item1aba483f6e:g:SrkAAOSwyXRgkc8n

$1699 42BO
https://www.ebay.com/itm/294121704192?hash=item447b050b00:g:CrIAAOSwVO5gdzdn

$2749, ‘mint’ 42BO
https://www.ebay.com/itm/333872841025?epid=22009472522&hash=item4dbc5f4141:g:kckAAOSwzdZgFFU1