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 in the picture below

`(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-8)}}} \implies \cfrac{-5 +3}{-4 +8} \implies \cfrac{ -2 }{ 4 } \implies - \cfrac{1 }{ 2 }`

`\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}{(-3)}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{(-8)}) \implies y +3 = - \cfrac{1 }{ 2 } ( x +8) \\\\\\ y+3=- \cfrac{1 }{ 2 }x-4\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x-7 \end{array}}`