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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+3,000 , 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 3,000 , 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+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.

1 answer

To create a linear function that models the relationship between the number of months (x) and the total amount of money (y) Oliwia will have in her account, we need to consider her initial deposit and the interest earned per month.

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

The total amount of money in her account after x months can be expressed as:

\[ y = \text{initial deposit} + \text{interest per month} \times \text{number of months} \]

Substituting the values we have:

\[ y = 3000 + 3x \]

This represents a linear function where:

  • The initial amount (intercept) is $3,000.
  • The slope (interest earned per month) is $3.

Thus, the correct equation is:

\[ y = 3x + 3000 \]

Now, looking at the response options, the correct choice is:

y = 3x + 3000, where x is the number of months and y is the total amount of money Oliwia will have in her account.