SOLUTION
Given
[tex]3x+4y=-2[/tex][tex]\begin{gathered} 4y=-3x-2 \\ \\ y=-\frac{3}{4}x-\frac{1}{2} \\ \\ m_1=-\frac{3}{4} \\ \end{gathered}[/tex]When two lines are perpendicular to each other, the product of their slopes is -1. Thus;
[tex]\begin{gathered} m_2=-\frac{1}{-\frac{3}{4}} \\ \\ m_2=\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]\frac{4}{3}[/tex]