Why do we use flex duct and plenum box for connecting supply duct to air terminals?

• flex  duct  is used to installed lengths runs short & to minimize the turns. it is very convenient for attaching supply air outlets to the rigid duct work .
• plenum box as an air mixing chamber before send  the air to the living spaces.it is a supply & exhaust of air through diffusers & grilles.plenum box intended to achieve a stable airflow in to a diff-user & also attenuate sound from the duct system.

your question was regarding the supply line thus we use the flexible duct to minimize the noise that may take place due the vibration when the machine is on.

Plenum duck is usually being used for the slot diffuser.

so simple flex ducts are flexible and cant design ducts for small areas. flex ducts are most commonly used in toilets because so many toilet chambers. plenum box for uniform flow through terminals

FLEXIBLE DUCT IS USED WHERE THE MINIMUM DISTANCE,   WHERE AS PELINIUM BOX IS TO STEP DOWN AND SUPPLY THE AIR OF AS  REQUIRED 

Flexible Ducts are use to damp / minimize vibration to be transferred from HVAC Ducts to False Ceiling.

Plenum box with sound liner are used to get:

• Uniform flow throughout the terminal, 
• Reduce Vibration and Sound

Flexible ducts in general has the following advantages:

1-the cost advantages of flex duct make it a popular choice for many builders.

2-in supply ducts to minimize vibration and noise

A plenum is an air-distribution box attached directly to the supply outlet of the HVAC equipment that heats or cools the air to make the house comfortable. The ductwork that distributes the heated or cooled air to individual rooms of the house connects to the plenum. The HVAC equipment has a blower that forces heated or cooled air into the supply plenum and from the plenum into the rooms through the supply duct system. Air-cleaning filters may be located in the supply plenum.