Let's analyze the given cost function for the gym membership, which is represented by the equation:
\[ \text{Cost} = 25 + 5x \]
where \( x \) is the number of visits to the gym.
a) The y-intercept
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:
\[ \text{Cost} = 25 + 5(0) = 25 \]
Thus, the y-intercept is 25.
This means that if a person does not visit the gym at all (0 visits), the cost of the gym membership is 25. This can be interpreted as the fixed cost or base membership fee that one would have to pay regardless of the number of visits.
b) The slope
The slope of the equation is the coefficient of \( x \), which is 5.
This means that for each additional visit to the gym (each increase in \( x \) by 1), the cost of the gym membership increases by 5. In other words, each visit to the gym incurs an additional cost of 5.
Summary:
- a) The y-intercept is 25. This means that the cost is 25 when there are no visits to the gym.
- b) The slope is 5. This means that for each visit to the gym, the cost increases by 5.
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