Question
The table below shows the amount that must be repaid, y, when x dollars are borrowed.
Amount Borrowed Amount Repaid
$100 $135
$200 $260
$500 $635
$800 $1,010
(1 point)
Responses
y=4/5x
y=5/4x+10
y=45x+55
Amount Borrowed Amount Repaid
$100 $135
$200 $260
$500 $635
$800 $1,010
(1 point)
Responses
y=4/5x
y=5/4x+10
y=45x+55
Answers
GPT-4o mini
To find the correct equation that relates the amount borrowed (x) to the amount repaid (y), we can analyze the given data.
From the table:
- When \( x = 100 \), \( y = 135 \)
- When \( x = 200 \), \( y = 260 \)
- When \( x = 500 \), \( y = 635 \)
- When \( x = 800 \), \( y = 1010 \)
We can observe the relationship between x and y.
First, let's see the ratios:
1. For \( x = 100 \),
\[ y = 135 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{135}{100} = 1.35 \]
2. For \( x = 200 \),
\[ y = 260 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{260}{200} = 1.3 \]
3. For \( x = 500 \),
\[ y = 635 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{635}{500} = 1.27 \]
4. For \( x = 800 \),
\[ y = 1010 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{1010}{800} = 1.2625 \]
These ratios suggest that \( y \) is increasing at a rate larger than \( x \), which indicates a linear relationship.
Let’s look closer at the differences:
- The increase when moving from \( x = 100 \) to \( x = 200 \) (from 135 to 260) is \( 260 - 135 = 125 \).
- From \( x = 200 \) to \( x = 500 \) (from 260 to 635) is \( 635 - 260 = 375 \).
- From \( x = 500 \) to \( x = 800 \) (from 635 to 1010) is \( 1010 - 635 = 375 \).
Thus, we will find an equation that holds for these numbers.
Now, let’s clarify the available options:
1. \( y = \frac{4}{5}x \): This is a decreasing function.
2. \( y = \frac{5}{4}x + 10 \): which indicates that for every dollar borrowed, 1.25 is repaid plus 10.
3. \( y = 45x + 55 \): This would indicate a very rapid repayment compared to borrowed amount, which does not match our data.
After solving or estimating the relationships, we notice that the best fitting among the choices provided and matched by reasoning suggests:
\( y = \frac{5}{4}x + 10 \).
This means effectively, for each dollar you borrow, you need to pay back 1.25 + an additional fee of 10.
Therefore, the answer is:
** \( y = \frac{5}{4}x + 10 \)**.
From the table:
- When \( x = 100 \), \( y = 135 \)
- When \( x = 200 \), \( y = 260 \)
- When \( x = 500 \), \( y = 635 \)
- When \( x = 800 \), \( y = 1010 \)
We can observe the relationship between x and y.
First, let's see the ratios:
1. For \( x = 100 \),
\[ y = 135 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{135}{100} = 1.35 \]
2. For \( x = 200 \),
\[ y = 260 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{260}{200} = 1.3 \]
3. For \( x = 500 \),
\[ y = 635 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{635}{500} = 1.27 \]
4. For \( x = 800 \),
\[ y = 1010 \]
\[ \text{Ratio} = \frac{y}{x} = \frac{1010}{800} = 1.2625 \]
These ratios suggest that \( y \) is increasing at a rate larger than \( x \), which indicates a linear relationship.
Let’s look closer at the differences:
- The increase when moving from \( x = 100 \) to \( x = 200 \) (from 135 to 260) is \( 260 - 135 = 125 \).
- From \( x = 200 \) to \( x = 500 \) (from 260 to 635) is \( 635 - 260 = 375 \).
- From \( x = 500 \) to \( x = 800 \) (from 635 to 1010) is \( 1010 - 635 = 375 \).
Thus, we will find an equation that holds for these numbers.
Now, let’s clarify the available options:
1. \( y = \frac{4}{5}x \): This is a decreasing function.
2. \( y = \frac{5}{4}x + 10 \): which indicates that for every dollar borrowed, 1.25 is repaid plus 10.
3. \( y = 45x + 55 \): This would indicate a very rapid repayment compared to borrowed amount, which does not match our data.
After solving or estimating the relationships, we notice that the best fitting among the choices provided and matched by reasoning suggests:
\( y = \frac{5}{4}x + 10 \).
This means effectively, for each dollar you borrow, you need to pay back 1.25 + an additional fee of 10.
Therefore, the answer is:
** \( y = \frac{5}{4}x + 10 \)**.