Question

Write an equation in standard form of the line With slope 2/5 and going through (-3,6).

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

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{\cfrac{2}{5}}(x-\stackrel{x_1}{(-3)})\implies y-6=\cfrac{2}{5}(x+3)$

$y-6=\cfrac{2}{5}x+\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-6)~~ = ~~5\left( \cfrac{2}{5}x+\cfrac{6}{5} \right)}\implies 5y-30~~ = ~~2x+6 \\\\\\ -2x+5y-30=6\implies -2x+5y=36\implies 2x-5y=-36$