
![\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-(-1)=\cfrac{6}{7}[x-(-3)] \\\\\\ y+1=\cfrac{6}{7}(x+3)\implies y+1=\cfrac{6}{7}x+\cfrac{18}{7}\implies y=\cfrac{6}{7}x+\cfrac{18}{7}-1 \\\\\\ y=\cfrac{6}{7}x+\cfrac{11}{7}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%28-1%29%3D%5Ccfrac%7B6%7D%7B7%7D%5Bx-%28-3%29%5D%20%5C%5C%5C%5C%5C%5C%20y%2B1%3D%5Ccfrac%7B6%7D%7B7%7D%28x%2B3%29%5Cimplies%20y%2B1%3D%5Ccfrac%7B6%7D%7B7%7Dx%2B%5Ccfrac%7B18%7D%7B7%7D%5Cimplies%20y%3D%5Ccfrac%7B6%7D%7B7%7Dx%2B%5Ccfrac%7B18%7D%7B7%7D-1%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B6%7D%7B7%7Dx%2B%5Ccfrac%7B11%7D%7B7%7D)
now, let's bear 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
so, let's multiply both sides by the LCD of all fractions, in this case that'd be 7, to do away with the denominators.
![\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7(y)=7\left( \cfrac{6}{7}x+\cfrac{11}{7} \right)}\implies 7y=6x+11\implies -6x+7y=11 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 6x-7y=-11~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B7%7D%7D%7B7%28y%29%3D7%5Cleft%28%20%5Ccfrac%7B6%7D%7B7%7Dx%2B%5Ccfrac%7B11%7D%7B7%7D%20%5Cright%29%7D%5Cimplies%207y%3D6x%2B11%5Cimplies%20-6x%2B7y%3D11%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%206x-7y%3D-11~%5Chfill)