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}{-5}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{(-5)}}} \implies \cfrac{-12}{5 +5} \implies \cfrac{ -12 }{ 10 } \implies - \cfrac{ 6 }{ 5 }`

`\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}{4}=\stackrel{m}{- \cfrac{ 6 }{ 5 }}(x-\stackrel{x_1}{(-5)}) \implies y -4 = - \cfrac{ 6 }{ 5 } ( x +5) \\\\\\ y-4=- \cfrac{ 6 }{ 5 }x-6\implies {\Large \begin{array}{llll} y=- \cfrac{ 6 }{ 5 }x-2 \end{array}}`