Question

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

Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer: ?

Answer 1

`(\stackrel{x_1}{9}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{9}}} \implies \cfrac{4 +1}{-16} \implies \cfrac{ 5 }{ -16 } \implies - \cfrac{ 5 }{ 16 }`

`\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}{(-1)}=\stackrel{m}{- \cfrac{ 5 }{ 16 }}(x-\stackrel{x_1}{9}) \implies y +1 = - \cfrac{ 5 }{ 16 } ( x -9)`