[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{8+4}{2}~~,~~\cfrac{-4-6}{2} \right)\implies (6,-5) \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad \stackrel{\textit{the midpoint}}{(\stackrel{x_2}{6}~,~\stackrel{y_2}{-5})}[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-7}{6-(-6)}\implies \cfrac{-12}{6+6}\implies \cfrac{-12}{12}\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-7=-1[x-(-6)]\implies y-7=-1(x+6) \\\\\\ y-7=-x-6\implies y=-x+1[/tex]
