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=45x
y is equal to 4 fifths x

y=54x+10
y is equal to 5 fourths x plus 10

y=54x
y is equal to 5 fourths x

y=45x+55

Answer 1

To find the correct equation that represents the relationship between the amount borrowed (x) and the amount repaid (y), we'll analyze the data points provided in the table.

**Data:**
- When \(x = 100\), \(y = 135\)
- When \(x = 200\), \(y = 260\)
- When \(x = 500\), \(y = 635\)
- When \(x = 800\), \(y = 1010\)

### Finding the relationship:

1. **Determine the slope (m)** using two points:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Taking the first two points:
\[
m = \frac{260 - 135}{200 - 100} = \frac{125}{100} = 1.25
\]

This implies:
\[
m = \frac{5}{4}
\]

2. **Writing the linear equation** in the slope-intercept form \(y = mx + b\):
Since we have found that the slope \(m = \frac{5}{4}\), we can plug it into the equation:
\[
y = \frac{5}{4}x + b
\]

3. **Finding y-intercept (b)**:
We can substitute one of the known points to find \(b\). Using the first data point \((100, 135)\):
\[
135 = \frac{5}{4}(100) + b
\]
\[
135 = 125 + b
\]
\[
b = 135 - 125 = 10
\]

4. **Final equation**:
The linear equation is:
\[
y = \frac{5}{4}x + 10
\]

### Final Answer:
The correct response is:
**y = 54x + 10 (which corresponds to y = \frac{5}{4}x + 10)**.