Question

Write an equation of the line that passes through each pair of points (9, 4), (−1, −1)

Answer 1

`(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{9}}} \implies \cfrac{ -5 }{ -10 }\implies \cfrac{1}{2}`

`\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}{4}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{9}) \\\\\\ y-4=\cfrac{1}{2}x-\cfrac{9}{2}\implies y=\cfrac{1}{2}x-\cfrac{9}{2}+4\implies y=\cfrac{1}{2}x-\cfrac{1}{2}`