Question

Write the equation of the line that passes through the points (−9,−4) and (−5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

`(\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 4 }`

`\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}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}`