Check if relation exist and mark as Booked.

I'm new to Laravel, so bear with me if this is the easiest thing in the world. ;)

I've started on a booking system as my first test project learning Laravel.

I have Bookable items that have bookable_slots(time) for each day. And of course the slots can be booked by a user.

So without including every detail in this post.

The bookable_slots table:

id  | bookable_id | day | start_at
--- | ----------- | --- | --------
1   | 1           | 1   | 08:00:00
2   | 1           | 1   | 12:00:00
3   | 1           | 1   | 16:00:00

I know the 'day' and want to list all bookable slots for it. That part is easy and I've done it like this:

public static function getDaySlots($day)
    {
        $dayBookables = Bookable_slots::where('day', '=', $day->dayOfWeek)->get();

        return $dayBookables;
    }

! Notice that the 'start_at' field is a TIME column. So I guess I have to add the "chosen date" from the $day variable to the slots 'start_at' value before I can check.

Anyway.. I have a bookings table where the 'start_at' field is a DATETIME column:

id  | slot_id | start_at
--- | ------- | -------------------
1   | 1       | 2015-10-05 08:00:00
1   | 3       | 2015-10-05 16:00:00

The relations in the models:

// Bookable_slots

public function bookings()
    {
        return $this->hasMany('App\Booking', 'slot_id');
    }


// Booking

public function slot()
    {
        return $this->hasOne('App\BookableSlots');
    }

Now.. How can I check if there is a booking on a slot, on a specific date and mark it as booked in the getDaySlots return?