Question
The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.
Which statement describes the `x`-intercept of the graph?
(6, 25,000) (25,11,250)
Which statement describes the `x`-intercept of the graph?
(6, 25,000) (25,11,250)
Answers
GPT-4o mini
The \( x \)-intercept of a graph represents the point where the line crosses the \( x \)-axis, which occurs when the value of \( y \) (in this case, the remaining balance) is equal to zero.
To determine the \( x \)-intercept, we would typically look for the value of the \( x \) (number of monthly payments made) when the remaining balance is zero.
If we are given the points \( (6, 25,000) \) and \( (25, 11,250) \), we can analyze these points in the context of a linear relationship.
1. **Point (6, 25,000)**: This point indicates that after 6 monthly payments, the remaining balance is $25,000.
2. **Point (25, 11,250)**: This point indicates that after 25 monthly payments, the remaining balance is $11,250.
To find the \( x \)-intercept, we would need to find the equation of the line that connects these two points and determine when the remaining balance (y) equals zero.
However, based on the points provided, we can't directly calculate the \( x \)-intercept without a linear equation or additional data on the total loan amount and/or payments.
In essence, the \( x \)-intercept represents the number of monthly payments made when the loan is fully paid off, meaning the remaining balance is zero.
If you're looking for a conclusion based on the provided information without calculating the exact intercept:
- The \( x \)-intercept represents the total number of monthly payments that will be made until the loan balance is reduced to zero.
To summarize, the statement describing the \( x \)-intercept would be: "The \( x \)-intercept indicates the total number of monthly payments required to completely pay off the loan."
To determine the \( x \)-intercept, we would typically look for the value of the \( x \) (number of monthly payments made) when the remaining balance is zero.
If we are given the points \( (6, 25,000) \) and \( (25, 11,250) \), we can analyze these points in the context of a linear relationship.
1. **Point (6, 25,000)**: This point indicates that after 6 monthly payments, the remaining balance is $25,000.
2. **Point (25, 11,250)**: This point indicates that after 25 monthly payments, the remaining balance is $11,250.
To find the \( x \)-intercept, we would need to find the equation of the line that connects these two points and determine when the remaining balance (y) equals zero.
However, based on the points provided, we can't directly calculate the \( x \)-intercept without a linear equation or additional data on the total loan amount and/or payments.
In essence, the \( x \)-intercept represents the number of monthly payments made when the loan is fully paid off, meaning the remaining balance is zero.
If you're looking for a conclusion based on the provided information without calculating the exact intercept:
- The \( x \)-intercept represents the total number of monthly payments that will be made until the loan balance is reduced to zero.
To summarize, the statement describing the \( x \)-intercept would be: "The \( x \)-intercept indicates the total number of monthly payments required to completely pay off the loan."