From the given table we will use the two points (10, 4) and (15, 10) to find the slope of the line
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Let (x1, y1) = (10, 4) and (x2, y2) = (15, 10)
[tex]\begin{gathered} m=\frac{10-4}{15-10} \\ m=\frac{6}{5} \\ m=1.2 \end{gathered}[/tex]
The form of the linear equation is
[tex]y=mx+b[/tex]
substitute the value of m
[tex]y=1.2x+b[/tex]
To find b substitute x by 10 and y by 4
[tex]\begin{gathered} x=10,y=4 \\ 4=1.2(10)+b \\ 4=12+b \end{gathered}[/tex]
Subtract 12 from both sides
[tex]\begin{gathered} 4-12=12-12+b \\ -8=b \end{gathered}[/tex]
The equation of the line best fit is
[tex]\begin{gathered} y=1.2x+(-8) \\ y=1.2x-8 \end{gathered}[/tex]
At x = 40, substitute x by 40
[tex]\begin{gathered} y=1.2(40)-8 \\ y=48-8 \\ y=40 \end{gathered}[/tex]
The expected number of games own is 40 games
