well, we know is linear because the exponent for both variables is "1".
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 first off do away with the denominators, by multiplying both sides by the LCD of all fractions, in this case that'd be 6.
[tex]\bf \cfrac{x+4}{2}=\cfrac{y-4}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{x+4}{2} \right)=6\left( \cfrac{y-4}{3} \right)}\implies 3x+12=2y-8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 3x-2y=-20~\hfill[/tex]
