Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{4}}}{\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} \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{5}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -4 = - \cfrac{5}{6} ( x +6) \\\\\\ y-4=- \cfrac{5}{6}x-5\implies {\Large \begin{array}{llll} y=- \cfrac{5}{6}x-1 \end{array}}`