Question

Which equations of the three lines are parallel, perpendicular, or neither?

Answer 1

The given lines are

`6x-4y=8;y=(3)/(2)x+6;2y=3x+5`

Convert each equation in the form

`y=mx+c_{}`

Therefore it follows:

`\begin{gathered} 6x-4y=8\Rightarrow y=(3)/(2)x+2 \\ y=(3)/(2)x+6\Rightarrow y=(3)/(2)x+6 \\ 2y=3x+5\Rightarrow y=(3)/(2)x+(5)/(2) \end{gathered}`

Therefore the slopes of all three lines are:

`\begin{gathered} m_1=(3)/(2) \\ m_2=(3)/(2) \\ m_3=(3)/(2) \end{gathered}`

The slopes of all three lines are equal therefore all three lines are parallel with each other.

Therefore it follows that:

`l_1\parallel l_2\parallel l_3`