The following table represents the total cost, in dollars (y) to join a gym for x number of months. The cost includes a one-time joining fee of $10. Does the data in the table represent a proportional relationship or a non-proportional relationship? How do you know

let y' is the monthly cost to join the gym
∵ The cost includes a one-time joining fee 10$
∵ y' = y -10
                       for x = 1 ⇒   y' = 25 - 10 = 15  ⇒⇒⇒ (y'/x) = 15
                       for x = 2 ⇒   y' = 40 - 10 = 30  ⇒⇒⇒ (y'/x) = 15
                       for x = 3 ⇒   y' = 55 - 10 = 45  ⇒⇒⇒ (y'/x) = 15
                       for x = 4 ⇒   y' = 70 - 10 = 60  ⇒⇒⇒ (y'/x) = 15
                       for x = 5 ⇒   y' = 85 - 10 = 75  ⇒⇒⇒ (y'/x) = 15

∵ y'/x  = constant = 15  ⇒⇒⇒ y' = 15x
 
∴ y = y' + 10
   y = 15x +10

The last equation in the form ⇒⇒⇒ y = m x + c
Which represents a non-proportional relationship
So,
       The data in the table represent a non-proportional relationship.
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Another solution:
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A proportional relationship has the form y = m x
Or (y/x) = m = constant
So,
       By dividing the values of y by the values of x we will not get a constant value

  ∴   The data in the table represent a non-proportional relationship.