Answer: y = (1/7)x
Explanation:
Yes, there is a direct variation between the number of campers (y) and the number of counselors (x) at the summer camp. Direct variation occurs when two variables are related in such a way that their ratio remains constant.
In this case, the ratio of the number of campers to the number of counselors is always 7:1. This means that for every 7 campers, there is 1 counselor. We can express this relationship using the equation:
y = kx
Where:
y represents the number of campers.
x represents the number of counselors.
k is the constant of variation.
Since there is one counselor for every 7 campers, the constant of variation (k) is 1/7. Therefore, the equation of direct variation relating the number of campers (y) and the number of counselors (x) is: