Question

Select the correct answer. Samir created a scatter plot and drew a line of best fit, as shown.​

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}{3}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{3}}} \implies \cfrac{ -6 }{ 9 } \implies -\cfrac{2}{3}`

`\begin{array}c \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}{10}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-10=-\cfrac{2}{3}x+2\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x+12 \end{array}}`