Question

In a circle, the circumference and diameter vary directly. Which of the following equations would allow you to find the diameter of a circle with a circumference of 154 if you know that in a second circle the diameter is 14 when the circumference is 44?

Answer 1

"something" varies directly to "something else"
"something" = "some value" * "something else"
y = n * x

what's the value "n" or "variation constant"? we dunno
but we know that when the diameter is 14, the circumference is 44
d = diameter
c= circumference thus

c = n*d
c = 44, d = 14

44 = n * 14

solve for "n" to find the variation constant value
then plug it in the other circle's equation

Answer 2

"In a circle, the circumference and diameter vary directly" is another way of stating the familiar formula \[\pi*d\]
You could proceed from here merely by substituting the circumference C = 154 to determine the related diameter, d, or you could pretend you don't know that the proportionality constant is pi and solve C=k*d for k using the data pertaining to the second circle. Note that k = 44/14 comes out to approximately pi.