Question

You open a savings account with your summer savings of $3200. You plan on spending $650 each month for rent and other expenses throughout the school year. Write an equation for the balance in your account as a function of the number of months since you deposited your summer savings.

Answer 1

The balance in the savings account as a function of the number of months is represented by the equation B(m) = $3200 - $650m, where B(m) is the balance and m is the number of months since the initial deposit.

Step-by-step explanation:

The question involves creating a linear function to represent the balance in a savings account as a function of time, given an initial deposit and consistent monthly expenses. This is a practical application of a linear equation.

To write the equation for the balance in the account, you need to start with the initial amount deposited, which is $3200, and subtract the monthly expenses, $650, multiplied by the number of months since the deposit. This can be expressed as:

B(m) = $3200 - $650m

where B(m) represents the balance in the account after m months, and m is the number of months since the initial deposit.

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Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable.

If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.