Two lines are parallel if:
[tex]m1=m2[/tex]
Two lines are perpendicular if:
[tex]m1\cdot m2=-1[/tex]
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Let's rewrite the given equations in the slope-intercept form:
[tex]\begin{gathered} 3x-2y=5 \\ y=\frac{3}{2}x-\frac{5}{2} \\ -------- \\ 6y-9x=6 \\ y=\frac{3}{2}x+1 \end{gathered}[/tex]
Since:
[tex]\begin{gathered} m1=m2 \\ \frac{3}{2}=\frac{3}{2} \\ \end{gathered}[/tex]
We can conclude that the lines are parallel.
