Question

Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.

(-2,8), (-3,-6)
The equation of the line in the form Ax+By = C is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answer 1

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-2)}}} \implies \cfrac{-14}{-3 +2} \implies \cfrac{ -14 }{ -1 }\implies 14`

`\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}{8}=\stackrel{m}{14}(x-\stackrel{x_1}{(-2)}) \implies y -8= 14 (x +2) \\\\\\ y-8=14x+28\implies y=14x+36 \\\\\\ -14x+y=36\implies {\Large \begin{array}{llll} 14x-y=-36 \end{array}}`