The General Form of a line is:
[tex]Ax+By=C[/tex]The slope intercept form is:
[tex]y=mx+b[/tex]The equation given in general form is:
[tex]3x+4y=12[/tex]Let's isolate y on the left hand side and re-arrange the equation in slope-intercept form:
[tex]\begin{gathered} 3x+4y=12 \\ 4y=-3x+12 \\ y=\frac{-3x+12}{4} \\ y=\frac{-3x}{4}+\frac{12}{4} \\ y=-\frac{3}{4}x+\frac{12}{4} \\ y=-\frac{3}{4}x+3 \end{gathered}[/tex]The final answer:
[tex]y=-\frac{3}{4}x+3[/tex]