[tex]\begin{gathered} Points \\ (2.5,1)(5,2)(7.5,2)(7.5,3)(7.5,4)(10,5)(10,6)(12.5,6) \\ (15,7)(15,8)(17.5,5)(17.5,7)(20,9)(22.5,7)(22.5,9)(25,11) \\ y=ax+b \\ a=\frac{n\Sigma xy-\Sigma x\Sigma y}{n\Sigma x^2-(\Sigma x)^2} \\ b=\frac{\Sigma y-a\Sigma x}{n} \\ n=16 \\ \Sigma xy=1515 \\ \Sigma x\Sigma y=(217.5)(92)=20010 \\ \Sigma x^2=3656.25 \\ (\Sigma x)^2=(217.5)^2=47306.25 \\ a=\frac{(16)(1515)-20010}{(16)(3656.25)-47306.25} \\ a=0.38 \\ b=\frac{(92)-(0.38)(217.5)}{16} \\ b=0.58 \\ Hence \\ The\text{ linear equation is y=0.38x+0.58} \end{gathered}[/tex]
