Slope are the same
MRSb,c = MUb/MUc = Pb/Pc
Utility Mazimizing Condition
MRSb,c = MUb/MUc = Pb/Pc --> MUb/Pb = MUc/Pc
The consumer is gonna make decisions up to the point where the ratio of the marginal utilities to the prices are equal
In case the consumer has two goods or more goods,the conditions hold.
MUa/Pa = MUb/Pb