Luther wants to get in shape, so he joins a local gym, Buff and Tough. For membership, the gym charges a registration fee plus monthly dues.

To determine if \( x \) (the number of months) and \( y \) (the total cost in dollars) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all values of \( x \).

Let's calculate the ratio for each pair of \( (x, y) \):

1. For \( x = 2 \), \( y = 49 \): \[ \frac{49}{2} = 24.5 \]

2. For \( x = 3 \), \( y = 65 \): \[ \frac{65}{3} \approx 21.67 \]

3. For \( x = 4 \), \( y = 81 \): \[ \frac{81}{4} = 20.25 \]

4. For \( x = 5 \), \( y = 97 \): \[ \frac{97}{5} = 19.4 \]

Now we can see that the ratios are not constant:

• \( \frac{49}{2} = 24.5 \)
• \( \frac{65}{3} \approx 21.67 \)
• \( \frac{81}{4} = 20.25 \)
• \( \frac{97}{5} = 19.4 \)

Since the ratio \( \frac{y}{x} \) changes with different values of \( x \), \( x \) and \( y \) do not have a proportional relationship.

Thus, the answer is no.