[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{10em}y=\stackrel{\downarrow }{\cfrac{6}{7}}x\underset{\uparrow }{-2}[/tex]
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, that way we do away with the denominators.
[tex]\bf \stackrel{\textit{multiplying by }\stackrel{LCD}{7}}{7(y)=7\left( \cfrac{6x}{7}-2 \right)}\implies 7y=6x-14 \\\\\\ -6x+7y=-14\implies \blacktriangleright 6x-7y=14 \blacktriangleleft[/tex]
