Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To understand what the \( y \)-intercept represents in this context, let’s carefully analyze the given equation:
[tex]\[ y = 75x + 50 \][/tex]
In this equation:
- \( y \) represents the total amount of money in Mario's account.
- \( x \) represents the number of monthly deposits.
- The coefficient \( 75 \) is the amount of money Mario deposits each month.
- The constant \( 50 \) is the \( y \)-intercept of the equation.
### Understanding the \( y \)-Intercept:
1. Definition: The \( y \)-intercept in a linear equation \( y = mx + b \) is the point where the line crosses the \( y \)-axis. This happens when \( x = 0 \).
2. Interpretation in the Context: When \( x = 0 \), this means that no monthly deposits have been made yet. Therefore, the \( y \)-intercept represents the initial amount of money in the account before any additional deposits.
### Applying to the Given Situation:
- According to the equation \( y = 75x + 50 \), when \( x = 0 \):
[tex]\[ y = 75 \cdot 0 + 50 \][/tex]
[tex]\[ y = 50 \][/tex]
- This initial amount of \( \$50 \) is the money Mario had in his account before making any monthly deposits.
### Conclusion:
From these observations, we can conclude that the \( y \)-intercept (which is \( 50 \)) represents the initial amount of money Mario received for his birthday, before any monthly deposits were made.
### Answer:
The correct interpretation is:
C. He was given \$50 for his birthday.
This means the [tex]\( \$50 \)[/tex] accounts for the birthday money Mario started with in his account.
[tex]\[ y = 75x + 50 \][/tex]
In this equation:
- \( y \) represents the total amount of money in Mario's account.
- \( x \) represents the number of monthly deposits.
- The coefficient \( 75 \) is the amount of money Mario deposits each month.
- The constant \( 50 \) is the \( y \)-intercept of the equation.
### Understanding the \( y \)-Intercept:
1. Definition: The \( y \)-intercept in a linear equation \( y = mx + b \) is the point where the line crosses the \( y \)-axis. This happens when \( x = 0 \).
2. Interpretation in the Context: When \( x = 0 \), this means that no monthly deposits have been made yet. Therefore, the \( y \)-intercept represents the initial amount of money in the account before any additional deposits.
### Applying to the Given Situation:
- According to the equation \( y = 75x + 50 \), when \( x = 0 \):
[tex]\[ y = 75 \cdot 0 + 50 \][/tex]
[tex]\[ y = 50 \][/tex]
- This initial amount of \( \$50 \) is the money Mario had in his account before making any monthly deposits.
### Conclusion:
From these observations, we can conclude that the \( y \)-intercept (which is \( 50 \)) represents the initial amount of money Mario received for his birthday, before any monthly deposits were made.
### Answer:
The correct interpretation is:
C. He was given \$50 for his birthday.
This means the [tex]\( \$50 \)[/tex] accounts for the birthday money Mario started with in his account.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.