Marsh Bright
11/23/2023 · Middle School
Question A high school freshman decided to start saving for college. Each week, \( \$ 35 \) is deposited into an account that starts with \( \$ 450 \). What is the \( y \)-intercept in this situation? Do not include units in your answer.
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In this situation, we can model the amount of money in the account as a linear function of the number of weeks. The equation for the total amount \( A \) in the account after \( t \) weeks can be expressed as:
\[
A(t) = 35t + 450
\]
Here, \( 35t \) represents the total amount deposited after \( t \) weeks, and \( 450 \) is the initial amount in the account.
In the context of a linear equation \( y = mx + b \), where \( b \) is the \( y \)-intercept, we can identify the \( y \)-intercept from our equation. The \( y \)-intercept occurs when \( t = 0 \):
\[
A(0) = 35(0) + 450 = 450
\]
Thus, the \( y \)-intercept in this situation is:
\[
\boxed{450}
\]
Quick Answer
450
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