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.
1 answer