如何从其他方法访问变量？ 或者如何做得更好？

I would like to know if there is any other way than to repeat my request in my controller. I have a function show($slug) with a query inside that takes the variable $teacher.

protected function show($slug)
{
    $teacher = Teacher::where('slug', $slug)->firstOrFail();

    return view('posts.postTeacher', [
        'teacher' => $teacher,
        'imageProfile' => $this->getImageProfile($slug)
    ]);
}

I created another function to manage my image. Only, I don't know how to access the varialbe $teacher of the other method. Then I am obliged to create a new one with the $slug too.

public function getImageProfile($slug)
{
    $teacher = Teacher::where('slug', $slug)->firstOrFail();

    $basePath = 'uploads/teachers/';
    $fullname = pathinfo($teacher->picture, PATHINFO_FILENAME);
    $imageProfile = $basePath . $fullname . '_profile.jpg';

    return $imageProfile;
}

Is there a better way to do this?

Why not just move getImageProfile inside Teacher-class?

class Teacher extends Model {

    // ....

    public function getImageProfile()
    {
        $basePath = 'uploads/teachers/';
        $fullname = pathinfo($this->picture, PATHINFO_FILENAME);
        return $basePath . $fullname . '_profile.jpg';
    }

}

and

protected function show($slug) {
    $teacher = Teacher::where('slug', $slug)->firstOrFail();

    return view('posts.postTeacher', [
        'teacher' => $teacher,
        'imageProfile' => $teacher->getImageProfile()
    ]);
}

Grouping logical things together, make the usage easier

Your second method could take the $fullname as an input argument:

protected function show($slug)
{
    $teacher = Teacher::where('slug', $slug)->firstOrFail();
    $fullname = pathinfo($teacher->picture, PATHINFO_FILENAME);

    return view('posts.postTeacher', [
        'teacher' => $teacher,
        'imageProfile' => $this->getImageProfile($slug, $fullname)
    ]);
}

public function getImageProfile($slug, $profilePrefix)
{
    $basePath = 'uploads/teachers/';
    $imageProfile = $basePath . $profilePrefix . '_profile.jpg';

    return $imageProfile;
}

You should be able to do this with Route-Model Binding (as described here). You can add a method to your teacher model that specifies that you're using a slug (instead of an id, which is the default):

public function getRouteKeyName()
{
    return 'slug';
}

With this you can setup your routes to look for the slug and pull up the appropriate instance of the teacher model for use in your controller methods.

// in your routes file
Route::get('teachers/{teacher}', 'TeachersController@show');

// in your controller
protected function show(Teacher $teacher)
{
    $imageProfile = $teacher->getImageProfile();
    return view('posts.postTeacher', compact('teacher', 'imageProfile'));
}

// in model
public function getImageProfile()
{
    $basePath = 'uploads/teachers/';
    $fullname = pathinfo($this->picture, PATHINFO_FILENAME);
    $imageProfile = $basePath . $fullname . '_profile.jpg';

    return $imageProfile;
}