Question

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, -3).

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-4)}}}\implies \cfrac{-10}{5+4}\implies -\cfrac{10}{9}`

`\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}{7}=\stackrel{m}{-\cfrac{10}{9}}(x-\stackrel{x_1}{(-4)})\implies y-7=-\cfrac{10}{9}(x+4)`