Question

What equation(s) represent (0,6) , (9,0)

Answer 1

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{0}}} \implies \cfrac{ -6 }{ 9 } \implies - \cfrac{ 2 }{ 3 }`

`\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}{6}=\stackrel{m}{- \cfrac{ 2 }{ 3 }}(x-\stackrel{x_1}{0}) \\\\\\ y-6=- \cfrac{ 2 }{ 3 }x\implies \boxed{y=- \cfrac{ 2 }{ 3 }x+6}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( - \cfrac{ 2 }{ 3 }x+6 \right)} \\\\\\ 3y=-2x+18\implies \boxed{2x+3y=18}`