Question

Determine the equation of the line of fit

Y= 15x+70
Y= 15x+40
Y=30x+70
Y=30x+40

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{100}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{100}-\stackrel{y1}{70}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 30 }{ 2 } \implies 15`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{ 15}(x-\stackrel{x_1}{2}) \\\\\\ y-70=15x-30\implies {\Large \begin{array}{llll} y=15x+40 \end{array}}`