Question

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

Answer 1

The given lines are

$6x-4y=8;y=\frac{3}{2}x+6;2y=3x+5$

Convert each equation in the form

$y=mx+c_{}$

Therefore it follows:

$\begin{gathered} 6x-4y=8\Rightarrow y=\frac{3}{2}x+2 \\ y=\frac{3}{2}x+6\Rightarrow y=\frac{3}{2}x+6 \\ 2y=3x+5\Rightarrow y=\frac{3}{2}x+\frac{5}{2} \end{gathered}$

Therefore the slopes of all three lines are:

$\begin{gathered} m_1=\frac{3}{2} \\ m_2=\frac{3}{2} \\ m_3=\frac{3}{2} \end{gathered}$

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

Therefore it follows that:

$l_1\parallel l_2\parallel l_3$