Solution:
To find the line of best fit for the scatterplot, we pick points from the graph as shown below
From the graph,
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,8) \\ (x_2,y_2)\Rightarrow(1,9) \end{gathered}[/tex]
To find the equation of a straight line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates into the formula above
[tex]\begin{gathered} \frac{y-8}{x-2}=\frac{9-8}{1-2} \\ \frac{y-8}{x-2}=\frac{1}{-1} \\ \frac{y-8}{x-2}=\frac{-1}{1} \\ Crossmultiply \\ 1(y-8)=-1(x-2) \\ y-8=-x+2 \\ y=-x+2+8 \\ y=-x+10 \end{gathered}[/tex]
Hence, the line of best fit is
[tex]y=-x+10[/tex]
