Question

Explain how to write an equation in point-slope form for the graph provided.

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 above.

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

`\begin{array}ll \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{4}{5}}(x-\stackrel{x_1}{(-2)}) \implies y -3 = -\cfrac{4}{5} ( x +2)`