1) Perpendicular lines have reciprocal and opposite slopes. But to properly check it, we need to rewrite the Standard form to the Slope-intercept
So let's rewrite it:
[tex]\begin{gathered} -3x+4y=-12 \\ 4y=-12+3x \\ y=-\frac{12}{4}+\frac{3}{4}x \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]2) Now, we can clearly see the slope. So now, we can tell that a perpendicular line would be reciprocal and opposite to the slope so we can tell that a perpendicular line will be:
[tex]m=-\frac{4}{3}[/tex]