Question

explain how you know the relationship between the admission fee for a group and the number of people in the group is linear

Answer 1

This function has the y-intercept (0,0).  What this means is that if there are no people in this group, no admission fee is payable.  For each new person added to the group, the total admission fee payable would increase by a fixed amount, which would be the unit fee per person (e. g., $5/person).