Mints cost 5 cents each and gumballs cost 3 cents each. Kathleen spent 60 cents buying x mints and y gumballs.

Slope intercept form:
y=-5/3+20

What is the y-intercept and what does it represent in this problem?

your equation only has one variable.

5x + 3y = 60
3y = -5x + 60
y = (-5/3)x + 20

the y intercept of 20 ( or y = 20)
gives you the number of gumballs (y) you can buy for 60 cents if you buy zero mints.