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Jerry was given some birthday money. He puts the money in an account. Every month after that, he deposits the same amount of money.

The equation that models this situation is [tex]\( y = 50x + 75 \)[/tex], where [tex]\( y \)[/tex] is the amount of money in the account and [tex]\( x \)[/tex] is the number of deposits.

What does the [tex]\( y \)[/tex]-intercept mean in this situation?

A. He puts [tex]\( \$75 \)[/tex] in the account each month.
B. He was given [tex]\( \$75 \)[/tex] for his birthday.
C. He puts [tex]\( \$50 \)[/tex] in the account each month.
D. He was given [tex]\( \$50 \)[/tex] for his birthday.

Sagot :

GinnyAnswer
To understand what the [tex]\( y \)[/tex]-intercept represents in this situation, let's analyze the given equation [tex]\( y = 50x + 75 \)[/tex].

The general form of a linear equation is [tex]\( y = mx + b \)[/tex], where:
- [tex]\( y \)[/tex] represents the dependent variable (in this case, the amount of money in the account).
- [tex]\( x \)[/tex] represents the independent variable (in this case, the number of deposits).
- [tex]\( m \)[/tex] represents the slope of the line (the amount of money deposited each month).
- [tex]\( b \)[/tex] represents the y-intercept (the initial amount of money in the account before any deposits are made).

In the equation [tex]\( y = 50x + 75 \)[/tex]:
- The slope [tex]\( m \)[/tex] is 50, which means Jerry deposits [tex]$50 into the account each month. - The y-intercept \( b \) is 75, which indicates the amount of money Jerry had in the account initially, before making any monthly deposits. The y-intercept occurs when \( x = 0 \), which means no deposits have been made yet. Therefore, the y-intercept of 75 represents the initial amount of money Jerry had in the account, which was given to him for his birthday. Thus, the correct interpretation is: B. He was given $[/tex]75 for his birthday.
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