Question

-4,-4 slope -3/2 in standard form

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}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{3}{2} \\\\\\ \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}{(-4)}=\stackrel{m}{-\cfrac{3}{2}}(x-\stackrel{x_1}{(-4)}) \implies y +4 = -\cfrac{3}{2} ( x +4)`

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y +4)=2\left( -\cfrac{3}{2} ( x +4) \right)}\implies 2y+8=-3(x+4)\implies 2y+8=-3x-12 \\\\\\ 3x+2y+8=-12\implies {\Large \begin{array}{llll} 3x+2y=-20 \end{array}}`