To identify the rate of change and initial value of the linear function representing the number of cards in Brian's collection, we need more information. Specifically, we need data points that relate the number of cards to another variable, such as time or money. With this information, we can calculate the slope (rate of change) and y-intercept (initial value) of the linear function.
For example, if we have data points such as:
- At time t=0, Brian had 50 cards
- At time t=1 year, Brian had 100 cards
- At time t=2 years, Brian had 150 cards
We can calculate the rate of change by finding the difference in the number of cards over the difference in time. In this case, the rate of change is (150-50)/(2-0) = 100/2 = 50 cards per year.
The initial value can be determined by observing the number of cards when t=0, which in this case is 50 cards.
In this scenario, the rate of change of 50 cards per year represents how Brian's card collection is increasing. The initial value of 50 cards represents the starting point or the number of cards Brian had initially.
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The number of cards in Brian's collection can be represented by a linear function. Identify the rate of change and initial value of this function. Explain what these values represent in terms of the situation.
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