For there to be a proportional relationship between circumference and area, the rate of change of the area to the circumference must be constant. Rate of change is the same as slope. The formula for determining slope is expressed as
Slope = (y2 - y1)/(x2 - x1)
From the table,
If x1 = 25, y1 = 50
if x2 = 31.5, y2 = 78.5
Slope = (78.5 - 50)/(31.5 - 25) = 28.5/6.5 = 4.38
If x1 = 31.5, y1 = 78.5
If x2 = 50, y2 = 201
Slope = (201 - 78.5)/(50 - 31.5) = 122.5/18.5 = 6.62
We can see that the slope or rate of change is not equal or constant. thus,
There is no proportional relationship between circumference and area
