How do I slow down a portion of a clip?

Bishop

For example, I have a 10 minute long clip. I want to slow the clip down to 1/2 speed from time 2:30 to 3:10. I also want to mute the sound during that period.

borate

Split the clip, at 2:30 and again at 3:10. Then right-click on the newly-split clip and CHANGE CLIP SPEED. Specify a speed or time. Right-click and MUTE CLIP.

Occasionally a speed-changed clip nestled amidst others does not work smoothly. In that case pre-produce the speed change for the clip - perhaps on another sequence - then export that sequence and add the clip back into the main sequence.