Abstract Noun:
* When referring to the general concept of incline or gradient:
* "The slopes of a mountain can be very challenging to climb." (Here, "slopes" refers to the idea of inclination itself)
* When referring to a mathematical concept:
* "In geometry, we study the slopes of lines." (Here, "slopes" refers to the mathematical concept of the rate of change)
Common Noun:
* When referring to specific, physical inclines:
* "The skiers enjoyed the long, smooth slopes." (Here, "slopes" refers to actual hills or inclines)
* When referring to a type of terrain:
* "The landscape was dominated by slopes and valleys." (Here, "slopes" refers to a type of terrain, like hills)
Therefore, the context determines whether "slopes" is an abstract or common noun.