Let's break down the given information based on the equation of the cost of a gym membership, represented by \( C(x) = 25 + 5x \), where \( C(x) \) is the total cost and \( x \) is the number of visits to the gym.
a) The y-intercept is ___.
The y-intercept of a linear equation is the value of \( C(x) \) when \( x = 0 \).
Setting \( x = 0 \) in the equation:
\[ C(0) = 25 + 5(0) = 25 \]
So, the y-intercept is 25. This means that if a person does not visit the gym at all (0 visits), they will still have to pay a registration cost of $25.
b) The slope is ___.
The slope of the equation is the coefficient of \( x \) in the linear equation. In this case, the slope is 5. This means that for each visit to the gym, the cost increases by $5.
Summary
- The y-intercept is 25. This means that the registration cost is $25 when there are no visits.
- The slope is 5. This means that it costs $5 for each visit to the gym.
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