Question

Write an equation of the line passing through ​(−3​,5​) and having slope −5. Give the answer in​ slope-intercept form.

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -5 \\\\\\ \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}{5}=\stackrel{m}{-5}(x-\stackrel{x_1}{(-3)}) \implies y -5 = -5 ( x +3) \\\\\\ y -5 = -5 x -15 \implies {\Large \begin{array}{llll} y = -5 x -10 \end{array}}`