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=45x+55
y is equal to 4 fifths x plus 55

y=54x
y is equal to 5 fourths x

y=54x+10

Answer 1

To determine the relationship between the amount borrowed (x) and the amount repaid (y), we can analyze the data given in the table.

We have the following pairs of values for (x, y):

1. (100, 135)
2. (200, 260)
3. (500, 635)
4. (800, 1010)

We can calculate the slope (m) from these points using the formula:

\[
m = \frac{\text{change in } y}{\text{change in } x}
\]

Calculating from the first two points:

\[
m = \frac{260 - 135}{200 - 100} = \frac{125}{100} = 1.25
\]

This means for every dollar borrowed, you repay $1.25.

Now let's calculate the y-intercept (b). We can use one of the points to solve for b. Using the point (100, 135):

\[
135 = 1.25(100) + b
\]
\[
135 = 125 + b
\]
\[
b = 135 - 125 = 10
\]

Thus, the equation that models the relationship between the amount borrowed and the amount repaid is:

\[
y = 1.25x + 10
\]

In terms of fractions, \(1.25\) can be represented as \(\frac{5}{4}\), so the equation is also:

\[
y = \frac{5}{4}x + 10
\]

We can verify this with other points:

For \(x = 200\):
\[
y = \frac{5}{4}(200) + 10 = 250 + 10 = 260 \quad \text{(correct)}
\]

For \(x = 500\):
\[
y = \frac{5}{4}(500) + 10 = 625 + 10 = 635 \quad \text{(correct)}
\]

For \(x = 800\):
\[
y = \frac{5}{4}(800) + 10 = 1000 + 10 = 1010 \quad \text{(correct)}
\]

So the correct answer is:

**y = \(\frac{5}{4}\)x + 10**

This can be summarized as:
- \(y = 54x + 10\) if \(y\) were to equal to \( \frac{5}{4} \), since multiplying through by 4 for easier use in other calculations would yield \(4y = 5x + 40\).

But from the given options, we see:

- The closest match is:

**y=54x+10**