Question

(-1,3)(2,5) find the standard form

Answer 1

keeping in mind that 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

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}}\implies \cfrac{2}{2+1}\implies \cfrac{2}{3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-1)}]\implies y-3=\cfrac{2}{3}(x+1) \\\\\\ y-3=\cfrac{2}{3}x+\cfrac{2}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( \cfrac{2}{3}x+\cfrac{2}{3} \right)}\implies 3y-9=2x+2 \\\\\\ 3y=2x+11\implies -2x+3y=11\implies 2x-3y=-11$