The given line in the question is
[tex]-3x-6y=30[/tex]Two lines are said to be parallel when their gradients or slope are equal
That is
[tex]m_1=m_2[/tex]The general equation of a line is given as
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \end{gathered}[/tex]Step 1: Make y the subject of the formula from the equation -3x-6y=30
[tex]\begin{gathered} -3x-6y=30 \\ \text{add 3x to both sides } \\ -3x+3x-6y=30+3x \\ -6y=3x+30 \\ \text{divide both sides by -6} \\ -\frac{6y}{-6}=\frac{3x}{-6}+\frac{30}{-6} \\ y=-\frac{1}{2}x-5 \end{gathered}[/tex]From the equation above by comparing coefficient, the slope is
[tex]m_1=-\frac{1}{2}[/tex]Step 2: Check which of the equations will have the same slope of -1/2
The first equation given in the question is
[tex]\begin{gathered} 2x-y=15 \\ \text{substract 2x from both sides} \\ 2x-2x-y=15-2x \\ -y=-2x+15 \\ \text{divide both sides by -1} \\ -\frac{y}{-1}=-\frac{2x}{-1}+\frac{15}{-1} \\ y=2x-15 \\ \text{the slope here is m =2} \end{gathered}[/tex]The second equation given is
[tex]\begin{gathered} 4y=20-2x \\ 4y=-2x+20 \\ \text{divide both sides by 4} \\ \frac{4y}{4}=-\frac{2x}{4}+\frac{20}{4} \\ y=-\frac{1}{2}x+5 \\ \text{the slope here is } \\ m=-\frac{1}{2} \end{gathered}[/tex]The third equation given is
[tex]\begin{gathered} x=18-2y \\ 2y=18-x \\ 2y=-x+18 \\ \text{divide all through by 2} \\ \frac{2y}{2}=-\frac{x}{2}+\frac{18}{2} \\ y=-\frac{1}{2}x+9 \\ \text{here the slope is} \\ m=-\frac{1}{2} \end{gathered}[/tex]The fourth equation given is
[tex]\begin{gathered} y=-3x+1 \\ \text{here the slope is} \\ m=-3 \end{gathered}[/tex]The fifth equation given is
[tex]\begin{gathered} 5x+10y=10 \\ \text{substract 5s from both sides} \\ 5x-5x+10y=10-5x \\ 10y=-5x+10 \\ \text{divide both sides by 10} \\ \frac{10y}{10}=-\frac{5x}{10}+\frac{10}{10} \\ y=-\frac{1}{2}x+1 \\ \text{here the slope is} \\ m=-\frac{1}{2} \end{gathered}[/tex]The sixth equation given is
[tex]\begin{gathered} 6-2y=4x \\ -2y=4x-6 \\ \text{divide both sides by -2} \\ -\frac{2y}{-2}=\frac{4x}{-2}-\frac{6}{-2} \\ y=-2x+3 \\ \text{here the slope is } \\ m=-2 \end{gathered}[/tex]Hence,
The equations parallel to -3x-6y=30 are
4y=20-2x
x=18-2y
5x+10y=10
