Answer :
We have the following:
We must pass each equation to the following form:
[tex]y=mx+b[/tex]where m is the slope
when two lines are parallel the slopes are equal, when they are perpendicular they are inverse
therefore,
[tex]\begin{gathered} -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]The slope is 4/5, the inverse is -5/4
now, for:
[tex]\begin{gathered} -x+5y=15 \\ 5y=x+15 \\ y=\frac{1}{5}x+3 \end{gathered}[/tex]therefore, they are neither parallel nor perpendicular
[tex]\begin{gathered} 7x+3y=-18 \\ 3y=-7x+18 \\ y=-\frac{7}{3}x+6 \end{gathered}[/tex]therefore, they are neither parallel nor perpendicular
[tex]\begin{gathered} -3x+7y=14 \\ 7y=3x+14 \\ y=\frac{3}{7}x+2 \end{gathered}[/tex]therefore, they are neither parallel nor perpendicular
[tex]\begin{gathered} 7x-3y=5 \\ 3y=7x-5 \\ y=\frac{7}{3}x-\frac{5}{3} \end{gathered}[/tex]therefore, they are neither parallel nor perpendicular
7x + 3y =-18 and - 3x + 7y = 14 are perpendicular
