How can I use a many-to-many relationship to display articles by tag in Laravel?

I am working on a blogging application in Laravel 8.

I am trying to display articles by tag at the following route:

Route::get('/tag/{tag_id}', [ArticlesController::class, 'tag'])->name('tag');

In the ArticlesController controller, I have the tag() method, which is supposed to display all posts that contain a certain tag:

public function tag($tag_id)
{
    $tag   = Tag::firstWhere('id', $tag_id);
    $articles = Article::where('id', $tag->id)->orderBy('id', 'desc')->paginate($this->per_page);

    return view(
      'themes/' . $this->theme_directory . '/templates/index',
      array_merge($this->data, [
        'tag'   => $tag,
        'articles' => $articles
      ])
    );
}

There is a many-to-many relationship between articles and tags. I have an article_tag pivot table:

In the Tag model I have:

class Tag extends Model
{
   use HasFactory;

   protected $fillable = ['name'];

   public function article()
   {
       return $this->belongsToMany(Article::class);
   } 
}

To the Article model I have added the tags() method

public function tags()
{
    return $this->belongsToMany(Tag::class)->as('tags');
}

The problem

The /tag/1 displays only one article and that article does not contain a tag with the id of 1.

Questions:

1. Where is my mistake?
2. What working solution requires minimal change in the current code?

It seems that the problem is that you take the article using the tag id, and do not check whether this tag is attached to the article where('id', $tag->id)

Try using whereHas in the articles query:

$articles = Article::whereHas('tags', function (Builder $query) use ($tag) {
  $query->where('id', $tag->id);
})->orderBy('id', 'desc')->paginate($this->per_page);

https://laravel.com/docs/8.x/eloquent-relationships