Question

Write an equation of the line passing through each of the following pairs of points.

(5, 7), (-6, -3)
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Answer 1

`\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{5}}}\implies \cfrac{-10}{-11}\implies \cfrac{10}{11}`

`\bf \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}{7}=\stackrel{m}{\cfrac{10}{11}}(x-\stackrel{x_1}{5})\implies y-7=\cfrac{10}{11}x-\cfrac{50}{11} \\\\\\ y=\cfrac{10}{11}x-\cfrac{50}{11}+7\implies y=\cfrac{10}{11}x+\cfrac{27}{11}`