Question

How do I make an equation on a graph?

Answer 1

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

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-10 +4}{6 +3} \implies \cfrac{ -6 }{ 9 } \implies - \cfrac{2 }{ 3 }`

`\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{2 }{ 3 }}(x-\stackrel{x_1}{(-3)}) \implies y +4 = - \cfrac{2 }{ 3 } ( x +3) \\\\\\ y+4=- \cfrac{2 }{ 3 }x-2\implies {\Large \begin{array}{llll} y=- \cfrac{2 }{ 3 }x-6 \end{array}}`