Question

Write the equation of the line that passes through the given points.
(-2,8.5) and (0,3.5)

Answer 1

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8.5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{8.5}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-5}{0 +2}\implies -\cfrac{5}{2}`

`\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}{8.5}=\stackrel{m}{- \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -8.5= -\cfrac{5}{2} (x +2) \\\\\\ y-8.5=-\cfrac{5}{2}x-5\implies y=-\cfrac{5}{2}x-5+8.5\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+3.5 \end{array}}`