• the Marginal Rate of  Substitution (MRS = MU_y/MU_x) equals the slope of the Budget Line ;

• the MRS also equals - (/P_x/P_y); and,

• a 'rationale' consumer will equate the MU per dollar of each commodity consumed, i.e. MU_x/P_x = MU_y/P_y .

The consumer cannot attain any higher indifference curve due to the income and price constraints.  The consumer could, of course, attain any point below but would not be rational to do so, i.e. their satisfaction would not be maximized.

In rare cases - a corner solution (M&Y 10th  Fig. 3.10; M&Y 11th Fig. 2.13; B&Z Fig. 3.12; B&B Fig. 4.7) - an individual will consume none of a commodity x because no amount of x is worth the cost. In such cases the consumer's maximum utility is obtained on the intercept of the y -axis, that is, no x is consumed

Ordinal utility indifference curves are based upon a set of psychological assumptions but they can also, theoretically, be derived from actual behaviour. By changing the budget line of a consumer and studying which commodity combinations are actually purchased one could theoretically derive an indifference curve for a consumer through 'revealed preference'. In practice, the necessary experiment is difficult if not  impossible to conduct in real life.