Question

Find the rule to the table​

Answer 1

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

$(\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}}\implies \cfrac{-10}{10}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-8=-x+2\implies \boxed{y=-x+10}$