Question

Write the equation of the line passing through the points(12,2) and
(-4,-2)

Answer 1

`(\stackrel{x_1}{12}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{12}}} \implies \cfrac{ -4 }{ -16 } \implies \cfrac{1}{4}`

`\begin{array}c \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}{4}}(x-\stackrel{x_1}{12}) \\\\\\ y-2=\cfrac{1}{4}x-3\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x-1 \end{array}}`