Question

What (-5, 2); m= 2/5 in standard form?

Answer 1

bearing 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}{-5}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{2}{5} \\\\\\ \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}{2}=\stackrel{m}{\cfrac{2}{5}}[x-\stackrel{x_1}{(-5)}]\implies y-2=\cfrac{2}{5}(x+5)`

`\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-2)=5\left[ \cfrac{2}{5}(x+5) \right]}\implies 5y-10=2(x+5)\implies 5y-10=2x+10 \\\\\\ 5y=2x+20\implies -2x+5y=20\implies \stackrel{\textit{standard form}}{2x-5y=-20}`