Question

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

The y-intercept is____________. This means that___________
The slope is__________. This means that_____________

Answer 1

To analyze the cost of a gym membership represented by the equation \( C(x) = 25 + 5x \), where \( C(x) \) is the cost and \( x \) is the number of visits to the gym, we can identify the y-intercept and slope.

1. **Y-Intercept**:
- The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:
\[
C(0) = 25 + 5(0) = 25
\]
- Thus, the y-intercept is **25**.
- **This means that** the cost of the gym membership is $25 when no visits are made. This represents a base fee or membership fee that must be paid regardless of the number of visits.

2. **Slope**:
- The slope of the line, represented by the coefficient of \( x \), is **5**.
- **This means that** for each additional visit to the gym (each increment of \( x \) by 1), the cost increases by $5. This represents the variable cost associated with each visit to the gym.

In summary:
- The y-intercept is **25**, meaning the base cost when not visiting the gym is $25.
- The slope is **5**, meaning each additional visit to the gym adds $5 to the total cost.