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.
(6, 25,500) (25, 11,250)
which statement describes the x-intercept of the graph?
a the x-intercept is 40, which represents the initial balance in dollars of the loan
b the x-intercept is 30,000, which represents the initial balance in dollars of the loan
c the x-intercept is 40, which represents the number of monthly payments needed to repay the loan
d the x-intercept is 30,000, which represents the number of monthly payments needed to repay the loan
(6, 25,500) (25, 11,250)
which statement describes the x-intercept of the graph?
a the x-intercept is 40, which represents the initial balance in dollars of the loan
b the x-intercept is 30,000, which represents the initial balance in dollars of the loan
c the x-intercept is 40, which represents the number of monthly payments needed to repay the loan
d the x-intercept is 30,000, which represents the number of monthly payments needed to repay the loan
Answers
GPT-4o mini
To find the x-intercept of the graph, we need to analyze the two given points: (6, 25,500) and (25, 11,250). The x-value represents the number of monthly payments made, and the y-value represents the remaining balance on the loan.
To find the x-intercept, we are looking for the point where the remaining balance (y-value) becomes zero. At this point, the loan has been fully paid off, and the number of monthly payments corresponds to the x-intercept.
1. **Determine the equation of the line**: We can first find the slope (m) between the two points.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11,250 - 25,500}{25 - 6} = \frac{-14,250}{19} \approx -750
\]
2. **Use point-slope form** to create an equation. We'll use point (6, 25,500):
\[
y - 25,500 = -750(x - 6)
\]
Expanding this gives us:
\[
y - 25,500 = -750x + 4,500
\]
\[
y = -750x + 30,000
\]
3. **Find the x-intercept** by setting y = 0:
\[
0 = -750x + 30,000
\]
\[
750x = 30,000
\]
\[
x = \frac{30,000}{750} = 40
\]
The x-intercept is 40, which indicates the number of monthly payments needed to repay the loan.
Based on this analysis, the correct option is:
**c. the x-intercept is 40, which represents the number of monthly payments needed to repay the loan.**
To find the x-intercept, we are looking for the point where the remaining balance (y-value) becomes zero. At this point, the loan has been fully paid off, and the number of monthly payments corresponds to the x-intercept.
1. **Determine the equation of the line**: We can first find the slope (m) between the two points.
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11,250 - 25,500}{25 - 6} = \frac{-14,250}{19} \approx -750
\]
2. **Use point-slope form** to create an equation. We'll use point (6, 25,500):
\[
y - 25,500 = -750(x - 6)
\]
Expanding this gives us:
\[
y - 25,500 = -750x + 4,500
\]
\[
y = -750x + 30,000
\]
3. **Find the x-intercept** by setting y = 0:
\[
0 = -750x + 30,000
\]
\[
750x = 30,000
\]
\[
x = \frac{30,000}{750} = 40
\]
The x-intercept is 40, which indicates the number of monthly payments needed to repay the loan.
Based on this analysis, the correct option is:
**c. the x-intercept is 40, which represents the number of monthly payments needed to repay the loan.**