Equations of Linear Functions Quick Check

Question

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Question
Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point)
Responses

\(y=3x+1,000\), where \(x\) is the number of months and \(y\) is the total amount of money Oliwia will have in her account.
y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

\(y=3,000x+3\), where \(x\) is the number of months and \(y\) is the total amount of money Oliwia will have in her account.
y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

\(y=1,000x+3\), where \(x\) is the number of months and \(y\) is the total amount of money Oliwia will have in her account.
y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

\(y=3x+3,000\), where \(x\) is the number of months and \(y\) is the total amount of money Oliwia will have in her account.

Answer 1

To find the correct equation that models the relationship between the number of months \(x\) and the total amount of money \(y\) that Oliwia will have in her bank account, we start with the initial deposit and the interest earned.

1. Initial Deposit: Oliwia deposits $3,000.
2. Monthly Interest: She earns $3 per month.

The total amount of money \(y\) after \(x\) months can be calculated as:

\[ y = \text{{Initial Deposit}} + \text{{Monthly Interest}} \times \text{{Number of Months}} \]

Plugging in the values:

\[ y = 3000 + 3x \]

This means the correct equation is:

\[ y = 3x + 3000 \]

Thus, the correct answer from the given options is:

\(y = 3x + 3,000\), where \(x\) is the number of months and \(y\) is the total amount of money Oliwia will have in her account.