Question

State whether the given set of lines are parallel, perpendicular or neither.3x-2y=56y-9x=6The lines are Answer

Answer 1

Two lines are parallel if:

`m1=m2`

Two lines are perpendicular if:

`m1\cdot m2=-1`

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Let's rewrite the given equations in the slope-intercept form:

`\begin{gathered} 3x-2y=5 \\ y=(3)/(2)x-(5)/(2) \\ -------- \\ 6y-9x=6 \\ y=(3)/(2)x+1 \end{gathered}`

Since:

`\begin{gathered} m1=m2 \\ (3)/(2)=(3)/(2) \\ \end{gathered}`

We can conclude that the lines are parallel.