You either have to pre-process the images into the thumbnails so that they exist on your file server as individual files, or create a route that serves images at the requested size.
For instance, if you have a route like
Route::get('/thumbnails/{id}/{width}',ImagesController@show);
Then you could create an html tag in your blade file like
<img src="/thumbnails/1234/150">
The browser then parses the html and finds the img request. It then downloads image 1234. Your controller gets the image id and the required width
It can then reply with the image resolution that was requested by loading the image into memory, resizing it with Intervention and replying with the content.
In the interests of performance, you should pre-process the images at the sizes you need.