To find the equation of the line of best fit for the given data points (1, 5), (2, 9), (3, 10), (4, 10.5), and (5, 11), we can use the method of linear regression.
Using a spreadsheet calculator, you can calculate the slope \( m \) and the y-intercept \( b \) of the line in the form \( y = mx + b \).
-
Calculate the means of x and y:
- Mean of \( x \): \( \bar{x} = \frac{1 + 2 + 3 + 4 + 5}{5} = 3 \)
- Mean of \( y \): \( \bar{y} = \frac{5 + 9 + 10 + 10.5 + 11}{5} = 9.1 \)
-
Calculate the slope \( m \): \[ m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2} \]
After performing these calculations, we can find that: \( m \approx 5.05 \)
-
Calculate the y-intercept \( b \): \[ b = \bar{y} - m \cdot \bar{x} \] Plugging in the values: \[ b = 9.1 - (5.05 \cdot 3) \approx 1.35 \]
Thus, the equation of the line of best fit is approximately: \[ y = 5.05x + 1.35 \]
Therefore, the correct response is: y = 5.05x + 1.35