well, 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
so hmmm we have a fraction.... so let's multiply both sides by the LCD of all fractions to do away with denominators, hmmm say the LCD will just be 3, so we'll multiply both sides by that
[tex]\bf y-4=\cfrac{5}{3}(x+3)\implies y-4=\cfrac{5(x+3)}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-4)=3\left( \cfrac{5(x+3)}{3} \right)} \\\\\\ 3y-12=5(x+3)\implies 3y-12=5x+15\implies 3y=5x+27 \\\\\\ -5x+3y=27\implies 5x-3y=-27[/tex]
