Question

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

Answer 1

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 + cWhich represents a non-proportional relationshipSo,        The data in the table represent a non-proportional relationship.===============================================================Another solution:-----------------------A proportional relationship has the form y = m xOr (y/x) = m = constantSo,        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.

hope this helps! :-)