Let's begin by identifying key information given to us:
We have the best line of fit that is a straight line.
The equation of a straight line is given by the equation: y = mx + b
We will pick two coordinates that lie on the straight line to form the equation:
[tex]\begin{gathered} (x_1,y_1)=(5,30) \\ (x_2,y_2)=(30,70) \end{gathered}[/tex]
We will proceed to calculate the slope of the equation using the coordinates above. We have:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{70-30}{30-5} \\ m=\frac{40}{25}=\frac{8}{5} \\ \therefore m=\frac{8}{5} \end{gathered}[/tex]
Since slope (m) = 8/5, the equation of the line becomes:
[tex]\begin{gathered} y=mx+b \\ m=\frac{8}{5} \\ \Rightarrow y=\frac{8}{5}x+b \end{gathered}[/tex]
The y-intercept (where the straight line touches the y-axis) of the graph equals 22: b = 22
Therefore, the equation of the straight line thus becomes:
[tex]y=\frac{8}{5}x+22[/tex]
