Question

Write the equation of the line that passes through the points (4,7) and (1,9) in point-slope form.

Answer 1

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{9 -7}{1 -4} \implies \cfrac{ 2 }{ -3 } \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{4})$