Karma was given some birthday money. She puts the money in an account.

Question

Every month after that, she deposits the same amount of money.
The equation that models this situation is y = 75x + 60, where yis the amount
of money in the account and x is the number of deposits.
What does the y-intercept mean in this situation?
She puts $75 in the account each month.
B. She puts $60 in the account each month.
C. She was given $60 for her birthday.
D. She was given 375 for her birthday.

Answer 1

In the equation \( y = 75x + 60 \), the y-intercept occurs when \( x = 0 \). This represents the amount of money in the account before any monthly deposits are made, which is the initial amount that Karma has.

Looking at the equation, when \( x = 0 \) (i.e., before she starts making deposits), the equation simplifies to:

\[ y = 75(0) + 60 = 60 \]

This means that the y-intercept, which is 60, represents the amount of money in the account at the beginning, which is the amount she received for her birthday.

Therefore, the correct interpretation of the y-intercept in this context is:

C. She was given $60 for her birthday.