Question

Write an equation of the line that passes through each pair of points (3, 0 ) (1, -6)

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-6}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ -6 }{ -2 } \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}{0}=\stackrel{m}{3}(x-\stackrel{x_1}{3})\implies {\Large \begin{array}{llll} y = 3 x -9 \end{array}}`