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=54x y is equal to 5 fourths x y=54x+10 y is equal to 5 fourths x plus 10 y=45x+55 y is equal to 4 fifths x plus 55 y=45x y is equal to 4 fifths x

Answer 1

To find the equation that represents the relationship between the amount borrowed (x) and the amount that must be repaid (y), we need to analyze the given data points.

The data points given are:
- (100, 135)
- (200, 260)
- (500, 635)
- (800, 1010)

Let's look for a linear relationship of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Find the Slope (m)
To calculate the slope \( m \) between two points, we can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (100, 135) and (200, 260):
\[
m = \frac{260 - 135}{200 - 100} = \frac{125}{100} = 1.25
\]

This means \( m = \frac{5}{4} \).

### Find the Y-Intercept (b)
To find the y-intercept \( b \), we can use one of the points. Let's use (100, 135):
\[
y = mx + b \implies 135 = \frac{5}{4}(100) + b
\]
Calculating \( \frac{5}{4}(100) \):
\[
135 = 125 + b \implies b = 135 - 125 = 10
\]

### Form the Equation
Now we can write the equation:
\[
y = \frac{5}{4}x + 10
\]

### Check if it's Consistent with Other Points
Let's check if this equation holds true for other values like \( x = 200, 500, 800 \):
- 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 \( x = 800 \):
\[
y = \frac{5}{4}(800) + 10 = 1000 + 10 = 1010 \quad \text{(Correct)}
\]

### Conclusion
The equation that best fits the relationship in the table is:
\[
y = \frac{5}{4}x + 10
\]

Thus the correct response is: **y is equal to 5 fourths x plus 10.**