Question

Write the equation of the line that passes through the points left bracket, minus, 6, comma, 1, right bracket(−6,1) and left bracket, 6, comma, minus, 9, right bracket(6,−9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-9}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{ -10 }{6 +6} \implies \cfrac{ -10 }{ 12 } \implies -\cfrac{5}{6}`

`\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}{1}=\stackrel{m}{-\cfrac{5}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -1 = -\cfrac{5}{6} ( x +6) \\\\\\ y-1=-\cfrac{5}{6}x-5\implies {\Large \begin{array}{llll} y=-\cfrac{5}{6}x-4 \end{array}}`