Question

A line passes through point (-9, 3) and has a slope of 2/3

Write an equation in Ax+By = C form for this line.
Use integers for A, B, and C.

Answer 1

`(\stackrel{x_1}{-9}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \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}{3}=\stackrel{m}{\cfrac{2}{3}}(x-\stackrel{x_1}{(-9)}) \implies y -3 = \cfrac{2}{3} ( x +9)`

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( \cfrac{2}{3} ( x +9) \right)}\implies 3y-9=2(x+9)\implies 3y-9=2x+18 \\\\\\ -2x+3y-9=18\implies -2x+3y=27\implies {\Large \begin{array}{llll} 2x-3y=-27 \end{array}}`