In order to calculate the line of best fit, let's start calculating the mean value of x and y.
The mean is given by the sum of all values divided by the number of values.
So we have:
[tex]\begin{gathered} \bar{x}=\frac{\sum_{i\mathop{=}1}^nx_i}{n}=\frac{81}{9}=9\\ \\ \bar{y}=\frac{\sum_{i\mathop{=}1}^ny_i}{n}=\frac{2277}{9}=253 \end{gathered}[/tex]Now, let's calculate the slope of the line using the formula below:
[tex]m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}=13.95[/tex]And finally, calculating the y-intercept, we have:
[tex]\begin{gathered} b=\bar{y}-m\bar{x}\\ \\ b=253-13.95\cdot9\\ \\ b=253-125.55\\ \\ b=127.45 \end{gathered}[/tex]Therefore the equation is:
[tex]y=13.95x+127.45[/tex]