Which statement describes the y-intercept of the graph?
Understand the Problem
The question is asking which statement correctly describes the y-intercept of a graph that illustrates the relationship between the number of monthly payments on a loan and the remaining balance. The y-intercept typically represents the initial value or starting point of the dependent variable when the independent variable is zero.
Answer
B: The y-intercept is 27,000, which represents the initial balance in dollars of the loan.
Answer for screen readers
The correct answer is B: The y-intercept is 27,000, which represents the initial balance in dollars of the loan.
Steps to Solve
- Identify the y-intercept on the graph
To determine the y-intercept from the graph, look for the point where the line crosses the y-axis (remaining balance in dollars). The remaining balance represents the initial amount owed on the loan when no payments have been made.
- Read the y-intercept value
From the graph provided, observe that the line intersects the y-axis at approximately $27,000. This indicates that the initial balance of the loan is $27,000 when no payments have been made.
- Interpret the meaning of the y-intercept
The y-intercept represents the starting point for the dependent variable (remaining balance in dollars). Hence, it indicates that at the beginning (when the number of monthly payments is zero), the remaining balance is $27,000.
- Compare the options provided
Now, let's assess the options provided in the question:
- A states the y-intercept is 60 (incorrect).
- B states the y-intercept is 27,000, which represents the initial balance (correct).
- C states the y-intercept is 60, which represents the number of payments (incorrect).
- D states the y-intercept is 27,000, representing the number of payments (incorrect).
The correct answer is B: The y-intercept is 27,000, which represents the initial balance in dollars of the loan.
More Information
The y-intercept in a linear graph shows the initial value of the dependent variable when the independent variable is zero. In this case, it reflects the total amount owed on the loan before any payments are made.
Tips
- Misreading the graph: Sometimes, the positions of points can be misinterpreted. Always double-check where the line intersects the y-axis.
- Confusing axes: Ensure you understand which axis represents the remaining balance and which represents the number of payments.
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