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}{2})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{ 6 }{10 +5} \implies \cfrac{ 6 }{ 15 } \implies \cfrac{2}{5}`

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