To determine the equation of the line of best fit for the given data, we can use simple linear regression. However, I will guide you through the calculations based on the data provided in the table.
The points given are:
- (1, 5)
- (2, 9)
- (3, 10)
- (4, 10.5)
- (5, 11)
Using a spreadsheet calculator, you can apply the linear regression formula, which usually involves finding the slope (m) and y-intercept (b) in the equation \(y = mx + b\).
Here's how the calculations typically work out for such data:
- Calculate the averages of x and y.
- Use the formula for the slope \(m\): \[ m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2} \]
- Once you have \(m\), calculate the y-intercept \(b\) using: \[ b = \bar{y} - m\bar{x} \]
After performing these calculations (the details might vary depending on the spreadsheet you use), you will find:
- Slope (m) ≈ 1.35
- y-intercept (b) ≈ 5.05
Thus, the line of best fit for the data is approximately:
\[ y = 1.35x + 5.05 \]
Hence, the correct response is:
y = 1.35x + 5.05.