Question

Find the equation of the line that goes through the points (-15,70) and (5,10).

Answer 1

`(\stackrel{x_1}{-15}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{70}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-15)}}} \implies \cfrac{-60}{5 +15} \implies \cfrac{ -60 }{ 20 } \implies - 3`

`\begin{array}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}{70}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-15)}) \implies y -70= -3 (x +15) \\\\\\ y - 70 = -3x - 45\implies {\Large \begin{array}{llll} y = -3x+25 \end{array}}`