[tex]\bf 12x=3y+7\implies 12x-7=3y\implies \cfrac{12x-7}{3}=y\implies \cfrac{12x}{3}-\cfrac{7}{3}=y \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{4}x-\cfrac{7}{3}=y\qquad \impliedby \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}[/tex]
