Question

What is an equation of the line that passes through the points (6, -5) and
(8, -6)?

Answer 1

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{-6 +5}{2} \implies \cfrac{ -1 }{ 2 }`

`\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}{(-5)}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +5= -\cfrac{1}{2} (x -6) \\\\\\ y+5=-\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=-\cfrac{1}{2}x-2 \end{array}}`