Question

Write the equation of the line that passes through the points (5,-9) and (−7,7). Put your answer in fully simplified point-slope form

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{7}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{5}}} \implies \cfrac{7 +9}{-12} \implies \cfrac{ 16 }{ -12 }\implies -\cfrac{4}{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}{(-9)}=\stackrel{m}{-\cfrac{4}{3}}(x-\stackrel{x_1}{5}) \implies y +9= -\cfrac{4}{3} (x -5) \\\\\\ y+9=-\cfrac{4}{3}x+\cfrac{20}{3}\implies y=-\cfrac{4}{3}x+\cfrac{20}{3}-9\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-\cfrac{7}{3} \end{array}}`