Given the lines:
[tex]\begin{gathered} 3x+2y=7 \\ 4x-6y=-8 \end{gathered}[/tex]We express them in slope-intercept form:
[tex]\begin{gathered} 3x+2y=7\Rightarrow2y=7-3x\Rightarrow y=-\frac{3}{2}x+\frac{7}{2} \\ \\ 4x-6y=-8\Rightarrow6y=4x+8\Rightarrow y=\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]The slopes of these lines are:
[tex]\begin{gathered} m_1=-\frac{3}{2} \\ m_2=\frac{2}{3} \end{gathered}[/tex]Then:
[tex]m_1\cdot m_2=-1[/tex]This is the condition for perpendicular lines, so the lines are perpendicular.
