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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]$\$[/tex]75[tex]$ in the account each month.

B. He was given $[/tex]\[tex]$75$[/tex] for his birthday.

C. He puts [tex]$\$[/tex]50[tex]$ in the account each month.

D. He was given $[/tex]\[tex]$50$[/tex] for his birthday.

Sagot :

GinnyAnswer
To understand what the [tex]\( y \)[/tex]-intercept represents in the equation [tex]\( y = 50x + 75 \)[/tex], we'll break down the equation and examine its components related to Jerry's birthday money and monthly deposits.

The equation is written in the slope-intercept form of a linear equation, which has the general form [tex]\( y = mx + b \)[/tex]. Here, [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.

1. Identify the [tex]\( y \)[/tex]-intercept:
- In the equation [tex]\( y = 50x + 75 \)[/tex], the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is 75. This means that when [tex]\( x = 0 \)[/tex] (which indicates that no deposits have been made yet), the amount of money in the account ([tex]\( y \)[/tex]) is [tex]$75. 2. Interpret the \( y \)-intercept: - When \( x = 0 \), the equation \( y = 50x + 75 \) simplifies to \( y = 75 \). This value of $[/tex]75 is the initial amount of money in the account before any deposits are made.
- Hence, the [tex]\( y \)[/tex]-intercept of 75 represents the initial money Jerry had in his account before he started making monthly deposits.

3. Analyze the context:
- According to the situation, Jerry was given some birthday money, which he put into the account initially.
- The [tex]\( y \)[/tex]-intercept represents this initial amount, which aligns with the context of being given money as a starting balance.

4. Consider the answer choices:
- A. He puts [tex]$\$[/tex] 75[tex]$ in the account each month. This is incorrect because $[/tex]50x[tex]$ represents the monthly deposits, not $[/tex]75.
- B. He was given [tex]$\$[/tex] 75[tex]$ for his birthday. This is correct. The initial balance of $[/tex]75 represents the money given as birthday money.
- C. He puts [tex]$\$[/tex] 50[tex]$ in the account each month. This is partially correct about the monthly deposits but does not explain the \( y \)-intercept. - D. He was given $[/tex]\[tex]$ 50$[/tex] for his birthday. This is incorrect as it does not align with the [tex]\( y \)[/tex]-intercept of 75.

Therefore, the correct interpretation of the [tex]\( y \)[/tex]-intercept in this situation is:

B. He was given \$75 for his birthday.
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