Output an events first cateory name and slug using the EE_Term object.

event_category_from_id.php

<?php

// The Event ID.
$event_id = 42;

//Pull the event object using the ID.
$event = EEM_Event::instance()->get_one_by_ID($event_id);

//Check we have an instance of an EE_Event
if ( $event instanceof EE_Event ) {
	//Debug
	//d($event);

	//Pull the first EE_Term associated with the event.
	$first_event_cat = $event->first_event_category();
	
	//Check we have an instance of EE_Term
	if ( $first_event_cat instanceof EE_Term ) {
		//Debug
		//d($first_event_cat);

		/* Now we have an EE_Term object for that event */
		/* We can output values using the object */
		echo $first_event_cat->name();
		echo "</br>";
		echo $first_event_cat->slug();

	}

}