Question

A line goes through the points (3, -4) and (-1, 8). Write the equation of the line in point-slope

form. Show your work for full credit. (Show the steps for how you went from the two points, above,
to having the equation in point-slope form. All calculations must be written down.) You may not
use graphing to answer this question. Circle or highlight your answer

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{8 +4}{-4} \implies \cfrac{ 12 }{ -4 }\implies -3`

`\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}{(-4)}=\stackrel{m}{-3}(x-\stackrel{x_1}{3}) \implies {\large \begin{array}{llll} y +4= -3 (x -3) \end{array}}`