To find the equation of the line of best fit for the given data, we can use a spreadsheet calculator to perform a linear regression analysis. Based on the data provided, we will find the line of best fit and its equation.
The data points are:
- (1, 5)
- (2, 9)
- (3, 10)
- (4, 10.5)
- (5, 11)
After calculating the linear regression, we typically represent a line in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Assuming you raise the line of best fit computation on a spreadsheet, let's say it returns an equation similar to \( y = mx + b \). From common practice or simulation, one plausible equation could be \( y = 1.35x + 5.05 \), which looks consistent with our observed y-values. However, without specific calculation done here, we can’t definitively say what it would yield without the tools.
Given the provided options:
- y = 5.05x + 1.35
- y = 5x + 11
- y = 1.35x + 5.05
- y = x + 5
The option closest to the likely slope and intercept derived from linear regression based on typical outputs would be \( y = 1.35x + 5.05 \).
Thus, the answer is:
y = 1.35x + 5.05