Question

The cost of a gym membership can be represented by 25 + 5x, where x is the number of visits to the gym. (4 points)

a) The y-intercept is (Answer). This means that (Answer)

b) The slope is (Answer). This means that (Answer)

Answer 1

Let's break down the equation for the cost of the gym membership: \( C = 25 + 5x \), where \( C \) is the total cost and \( x \) is the number of visits to the gym.

### a) Y-Intercept
The y-intercept of a linear equation in the form \( y = mx + b \) occurs when \( x = 0 \). In this case, the y-intercept is:

- **Y-Intercept**: \( C = 25 + 5(0) = 25 \)
- So, the y-intercept is **(0, 25)**.

**This means that** if a person does not visit the gym at all (0 visits), they still have to pay a fixed cost of $25, which could be considered as a membership fee.

### b) Slope
The slope of the equation \( C = 25 + 5x \) is the coefficient of \( x \), which represents the increase in cost per additional visit to the gym.

- **Slope**: The slope is **5**.

**This means that** for each additional visit to the gym, the cost increases by $5.

### Final Answers
a) The y-intercept is **(0, 25)**. This means that **if there are no visits, the fixed membership fee is $25**.

b) The slope is **5**. This means that **the cost increases by $5 for each additional visit to the gym**.