Sergei chooses between baseball bats and cameras, and M is his utility-maximizing choice on the original budget constraint. A higher price for bats does not change how many cameras he could buy if he spent everything on cameras, so the vertical intercept stays put and the budget constraint rotates clockwise, as if on a hinge, to a smaller horizontal intercept.
The dashed lines through M divide the new constraint. At H he buys fewer bats and more cameras; at J less of both; at K exactly as many bats as before but fewer cameras, since K is straight below M. A choice like L, more bats at a higher price, is theoretically possible but ruled out in practice. The slider sets how much the price of bats rises; the axes are deliberately unnumbered, as in the book.