Question

Find an equation of the line passing through the given points. Use function notation to write the equation. ​(​-6,-2​) and ​(​-9,-1​)

Answer 1

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-9}-\underset{x_1}{(-6)}}} \implies \cfrac{-1 +2}{-9 +6} \implies \cfrac{ 1 }{ -3 } \implies -\cfrac{1}{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}{(-2)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +2 = -\cfrac{1}{3} ( x +6) \\\\\\ y+2=-\cfrac{1}{3}x-2\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x-4 \end{array}}`