Question
Flooring City is running a limited time special on carpeting. The cost to have your home carpeted is $100 per room and a $50 flat fee for installation.
Part II: Identify the
y-intercept of the equation you wrote in Part I. Then, state the meaning of the
y-intercept in terms of the problem situation.
Part II: Identify the
y-intercept of the equation you wrote in Part I. Then, state the meaning of the
y-intercept in terms of the problem situation.
Answers
GPT-4o mini
To identify the y-intercept in this situation, let's first write the equation representing the cost of carpeting your home.
Let:
- \( x \) = the number of rooms to be carpeted
- \( y \) = the total cost
The total cost \( y \) can be represented by the equation:
\[ y = 100x + 50 \]
Here, $100 is the cost per room, and $50 is the flat fee for installation.
### Y-intercept
In the equation \( y = 100x + 50 \), the y-intercept occurs when \( x = 0 \). To find the y-intercept:
\[ y = 100(0) + 50 \]
\[ y = 50 \]
### Meaning of the Y-intercept
The y-intercept of 50 means that if you have 0 rooms to carpet (i.e., you are not carpeting any rooms in your home), the total cost will still be $50. This amount represents the flat fee for installation that is charged regardless of the number of rooms being carpeted. Hence, if no carpeting is done, you still incur a cost of $50 for the installation service.
Let:
- \( x \) = the number of rooms to be carpeted
- \( y \) = the total cost
The total cost \( y \) can be represented by the equation:
\[ y = 100x + 50 \]
Here, $100 is the cost per room, and $50 is the flat fee for installation.
### Y-intercept
In the equation \( y = 100x + 50 \), the y-intercept occurs when \( x = 0 \). To find the y-intercept:
\[ y = 100(0) + 50 \]
\[ y = 50 \]
### Meaning of the Y-intercept
The y-intercept of 50 means that if you have 0 rooms to carpet (i.e., you are not carpeting any rooms in your home), the total cost will still be $50. This amount represents the flat fee for installation that is charged regardless of the number of rooms being carpeted. Hence, if no carpeting is done, you still incur a cost of $50 for the installation service.