Question

Write an equation of the line through (-1,-5) having slope 2/3. give the answer in 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

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-1)}]\implies y+5=\cfrac{2}{3}(x+1)$

$\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+5)=3\left( \cfrac{2}{3}(x+1) \right)}\implies 3y+15 = 2(x+1) \implies 3y+15=2x+2 \\\\\\ 3y=2x-13\implies -2x+3y=-13\implies 2x-3y=13$