The budget constraint shows every combination of T-shirts and movies José can afford. Its vertical intercept is income divided by the price of a movie ($56 / $7 = 8 movies) and its horizontal intercept is income divided by the price of a T-shirt ($56 / $14 = 4 T-shirts), so its slope is −8/4 = −2: each T-shirt costs two movies.
The lettered points are the combinations with whole numbers of each good. Moving the income or price sliders shifts or rotates the line and the affordable points move with it. The utility toggles add the total utility of each point from the chapter's table, which is how José finds that S, one T-shirt and six movies, is his best choice.